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1999-12-11 03:00:00
2025-04-28 00:58:08
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A383122
a(n) is the smallest number that can be expressed as the sum of the smallest number of powers with different exponents greater than one in n different ways (for unitary bases, the smallest possible exponents are considered).
[ "1", "16", "17", "65", "80", "105", "139", "193", "329", "313", "336", "410", "477", "273", "553", "461", "436", "1219", "942", "10153", "1595", "1038", "722", "636", "1769", "1344", "2045", "2381", "1805", "2379", "3683", "2365", "1611", "3319", "3815", "4416", "4838", "4029", "3531", "5606", "5789", "4411", "4341", "5849", "7392", "1642", "4885", "8246", "3074", "5251", "5774", "3165", "2498", "12347", "9987", "5405", "8075", "11101", "2346", "6749" ]
[ "nonn", "new" ]
11
1
2
[ "A351062", "A351063", "A351064", "A351065", "A351066", "A383122" ]
null
Alberto Zanoni, Apr 17 2025
2025-04-18T22:24:52
oeisdata/seq/A383/A383122.seq
a03bafd2626c3b4164448c887d26c65d
A383125
Number of cyclic edge cuts in the n-web graph.
[ "8", "48", "2592", "113856" ]
[ "nonn", "more", "new" ]
4
3
1
null
null
Eric W. Weisstein, Apr 17 2025
2025-04-17T08:11:16
oeisdata/seq/A383/A383125.seq
fdcf7188c699fb7118ebf6497a5e42c8
A383131
a(n) is the number of iterations that n requires to reach 1 under the map x -> -x/2 if x is even, 3x + 1 if x is odd; a(n) = -1 if 1 is never reached.
[ "0", "3", "12", "2", "5", "5", "8", "5", "11", "11", "50", "14", "14", "14", "53", "4", "17", "17", "43", "7", "7", "7", "20", "7", "46", "46", "59", "10", "10", "10", "23", "7", "49", "49", "62", "13", "13", "13", "13", "13", "26", "26", "39", "52", "52", "52", "65", "16", "16", "16", "78", "16", "16", "16", "29", "16", "42", "42", "55", "55", "55", "55", "68", "6", "19", "19", "19", "19", "19" ]
[ "nonn", "new" ]
13
1
2
[ "A006577", "A381055", "A383131" ]
null
Ya-Ping Lu, Apr 17 2025
2025-04-19T01:59:17
oeisdata/seq/A383/A383131.seq
00b4b2d73a97e05e6e1354d14e14330a
A383132
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) * n^k.
[ "1", "2", "33", "2701", "524993", "181752001", "97735073905", "75179269556672", "78240951854025217", "105806762566689176353", "180297512864534759056001", "377878889913778527874694227", "955217573424445946022789385537", "2865620569274978738097814056365899", "10064763360358683666070320479027168465" ]
[ "nonn", "new" ]
7
0
2
[ "A084771", "A187021", "A331656", "A340971", "A383120", "A383132", "A383133" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-19T05:17:12
oeisdata/seq/A383/A383132.seq
8b5adc546228656376c6976936a64d84
A383133
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) * n^k.
[ "1", "0", "17", "1889", "412225", "151448249", "84430503361", "66535567456546", "70456680210155009", "96530372235620300465", "166169585125820280654001", "351113456811120647774884511", "893491183170443755035588745153", "2695374684029443253628238600963667", "9511442599320236554084097413617603681" ]
[ "nonn", "new" ]
6
0
3
[ "A307885", "A331657", "A340972", "A383121", "A383132", "A383133" ]
null
Ilya Gutkovskiy, Apr 17 2025
2025-04-19T05:22:14
oeisdata/seq/A383/A383133.seq
3ff24537a7f1fa48d8433ddaebac6069
A383134
Array read by ascending antidiagonals: A(n,k) is the length of the arithmetic progression of only primes having difference n and first term prime(k).
[ "2", "1", "1", "2", "3", "1", "1", "1", "2", "1", "2", "3", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "5", "1", "1", "1", "2", "1", "2", "3", "1", "3", "1", "2", "1", "1", "1", "1", "1", "2", "1", "4", "1", "1", "1", "1", "1", "2", "3", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabl", "new" ]
12
1
1
[ "A000012", "A006512", "A040976", "A054977", "A088430", "A175191", "A206045", "A237453", "A383134" ]
null
Stefano Spezia, Apr 17 2025
2025-04-18T09:53:25
oeisdata/seq/A383/A383134.seq
02e4abda23fbdba3feba2c540e518a6b
A383136
a(n) = Sum_{k=0..n} k^2 * 2^(n-k) * binomial(n,k).
[ "0", "1", "8", "45", "216", "945", "3888", "15309", "58320", "216513", "787320", "2814669", "9920232", "34543665", "119042784", "406552365", "1377495072", "4634696961", "15496819560", "51526925037", "170465015160", "561372288561", "1841022163728", "6014703091725", "19581781196016", "63546645708225", "205608702558168" ]
[ "nonn", "easy", "new" ]
9
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:58
oeisdata/seq/A383/A383136.seq
4e68baf6407516237396c3e49026f7b0
A383137
a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).
[ "0", "1", "12", "87", "504", "2565", "11988", "52731", "221616", "898857", "3542940", "13640319", "51490728", "191141613", "699376356", "2527001955", "9030245472", "31955015889", "112093661484", "390132432423", "1348223301720", "4629287423061", "15802106905332", "53651151578187", "181257000301584" ]
[ "nonn", "easy", "new" ]
10
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:54
oeisdata/seq/A383/A383137.seq
28b97935ca8ee782f377ae87e1d404d1
A383138
a(n) = Sum_{k=0..n} k^4 * 2^(n-k) * binomial(n,k).
[ "0", "1", "20", "189", "1320", "7785", "41148", "201285", "929232", "4100625", "17452260", "72098829", "290521080", "1146082041", "4439303820", "16923738645", "63619864992", "236206924065", "867305334708", "3152957079645", "11359168737480", "40589657212041", "143957705302620", "507079568653029" ]
[ "nonn", "easy", "new" ]
10
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:50
oeisdata/seq/A383/A383138.seq
b0b362481919ed27e301d27c7792d3e4
A383139
a(n) = Sum_{k=0..n} k^5 * 2^(n-k) * binomial(n,k).
[ "0", "1", "36", "447", "3768", "25725", "153468", "832923", "4213296", "20179449", "92510100", "409137399", "1755881064", "7345518453", "30059956332", "120676965075", "476358203232", "1852442299377", "7108046758404", "26948581794351", "101065091563800", "375297714478701", "1381124599327836", "5040775635099147" ]
[ "nonn", "easy", "new" ]
8
0
3
[ "A027471", "A383136", "A383137", "A383138", "A383139" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-17T12:27:44
oeisdata/seq/A383/A383139.seq
70abc524d9ae58167060cdc76585314b
A383140
Triangle read by rows: the coefficients of polynomials (1/3^(m-n)) * Sum_{k=0..m} k^n * 2^(m-k) * binomial(m,k) in the variable m.
[ "1", "0", "1", "0", "2", "1", "0", "2", "6", "1", "0", "-6", "20", "12", "1", "0", "-30", "10", "80", "20", "1", "0", "42", "-320", "270", "220", "30", "1", "0", "882", "-1386", "-770", "1470", "490", "42", "1", "0", "954", "7308", "-15064", "2800", "5180", "952", "56", "1", "0", "-39870", "101826", "-39340", "-61992", "29820", "14364", "1680", "72", "1", "0", "-203958", "-40680", "841770", "-666820", "-86940", "139440", "34020", "2760", "90", "1" ]
[ "sign", "tabl", "new" ]
36
0
5
[ "A000007", "A027471", "A129062", "A133494", "A179929", "A209849", "A212846", "A383136", "A383137", "A383138", "A383139", "A383140" ]
null
Seiichi Manyama, Apr 17 2025
2025-04-18T08:44:25
oeisdata/seq/A383/A383140.seq
06016fc75d031b26767dd6e3047e21c4
A383142
Smallest positive integer with shortest addition-subtraction chain of length n.
[ "1", "2", "3", "5", "7", "11", "19", "29", "53", "87", "151", "267", "461", "811", "1383", "2357", "4277", "7499", "14003", "25931", "44269", "87773", "152947", "271563" ]
[ "nonn", "hard", "more", "new" ]
10
0
2
[ "A003064", "A128998", "A383001", "A383142", "A383143" ]
null
Jinyuan Wang, Apr 17 2025
2025-04-18T10:59:25
oeisdata/seq/A383/A383142.seq
eaf4520aa56a68038b2c0113a2d42521
A383143
Number of positive integers with a shortest addition-subtraction chain of length n.
[ "1", "1", "2", "3", "5", "9", "16", "28", "49", "88", "156", "280", "499", "904", "1639", "2986", "5442", "9936", "18134" ]
[ "nonn", "hard", "more", "new" ]
9
0
3
[ "A003065", "A128998", "A383002", "A383142", "A383143" ]
null
Jinyuan Wang, Apr 17 2025
2025-04-18T10:59:33
oeisdata/seq/A383/A383143.seq
81d2d65b91ee51677a80823332d128a5
A383144
Number of abelian/medial racks of order n, up to isomorphism.
[ "1", "1", "2", "6", "18", "68", "329", "1965", "15455", "155902", "2064870", "35982366", "832699635", "25731050872" ]
[ "hard", "more", "nonn", "new" ]
8
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A383144", "A383145", "A383146" ]
null
Luc Ta, Apr 17 2025
2025-04-24T16:51:00
oeisdata/seq/A383/A383144.seq
1110fd4108d289e309c9c4d4078ab30e
A383145
Number of GL-racks of order n, up to isomorphism.
[ "1", "1", "4", "13", "62", "308", "2132", "17268", "189373" ]
[ "hard", "more", "nonn", "new" ]
10
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A374939", "A374942", "A374943", "A374944", "A374945", "A374946", "A374947", "A383144", "A383145", "A383146" ]
null
Luc Ta, Apr 17 2025
2025-04-25T03:08:23
oeisdata/seq/A383/A383145.seq
393801fbfa9dedc1aa78e0db0539d9e6
A383146
Number of medial GL-racks of order n, up to isomorphism.
[ "1", "1", "4", "13", "61", "298", "2087", "16941", "187160" ]
[ "hard", "more", "nonn", "new" ]
8
0
3
[ "A165200", "A176077", "A177886", "A178432", "A179010", "A181769", "A181770", "A181771", "A193024", "A196111", "A198147", "A225744", "A226172", "A226173", "A226174", "A226193", "A236146", "A242044", "A242275", "A243931", "A248908", "A254434", "A257351", "A374939", "A374942", "A374943", "A374944", "A374945", "A374946", "A374947", "A383144", "A383145", "A383146" ]
null
Luc Ta, Apr 17 2025
2025-04-25T03:08:31
oeisdata/seq/A383/A383146.seq
b87400b1b879ebc4631dea0367284850
A383147
Sum of odd divisors m of n such that there is a divisor d of n with d < m < 2*d.
[ "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "3", "0", "0", "5", "0", "0", "12", "0", "5", "0", "0", "0", "3", "0", "0", "0", "7", "0", "23", "0", "0", "0", "0", "7", "12", "0", "0", "0", "5", "0", "31", "0", "0", "29", "0", "0", "3", "0", "0", "0", "0", "0", "39", "0", "7", "0", "0", "0", "23", "0", "0", "9", "0", "0", "47", "0", "0", "0", "7", "0", "12", "0", "0", "30", "0", "11", "42", "0", "5", "0", "0", "0", "31", "0", "0", "0", "11", "0", "77", "13", "0", "0", "0", "0" ]
[ "nonn", "new" ]
18
1
6
[ "A000593", "A237270", "A237271", "A237593", "A239657", "A379379", "A383147", "A383209" ]
null
Omar E. Pol, Apr 17 2025
2025-04-25T18:48:18
oeisdata/seq/A383/A383147.seq
cff0fb5f47a8ba596407c7a67bb32a68
A383148
k-facile numbers: Numbers m such that the sum of the divisors of m is equal to 2*m+s where s is a product of distinct divisors of m.
[ "12", "18", "20", "24", "30", "40", "42", "54", "56", "60", "66", "78", "84", "88", "90", "102", "104", "114", "120", "132", "138", "140", "168", "174", "186", "196", "204", "222", "224", "234", "246", "252", "258", "264", "270", "280", "282", "308", "312", "318", "348", "354", "360", "364", "366", "368", "380", "402", "414", "420", "426", "438", "440", "456", "464", "468", "474", "476" ]
[ "nonn", "new" ]
22
1
1
[ "A000203", "A000396", "A005101", "A181595", "A383148" ]
null
Joshua Zelinsky, Apr 17 2025
2025-04-24T18:27:20
oeisdata/seq/A383/A383148.seq
bccfa6402c91903971ea22f2d4eb13bb
A383149
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = (-1)^k * [m^k] (1/2^(m-n)) * Sum_{k=0..m} k^n * (-1)^m * 3^(m-k) * binomial(m,k).
[ "1", "0", "1", "0", "3", "1", "0", "12", "9", "1", "0", "66", "75", "18", "1", "0", "480", "690", "255", "30", "1", "0", "4368", "7290", "3555", "645", "45", "1", "0", "47712", "88536", "52290", "12705", "1365", "63", "1", "0", "608016", "1223628", "831684", "249585", "36120", "2562", "84", "1", "0", "8855040", "19019664", "14405580", "5073012", "915705", "87696", "4410", "108", "1" ]
[ "nonn", "tabl", "new" ]
35
0
5
[ "A000007", "A001787", "A122704", "A123227", "A129062", "A178987", "A209849", "A383140", "A383149", "A383150", "A383151", "A383152", "A383155", "A383163", "A383164" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:21
oeisdata/seq/A383/A383149.seq
eff235d093ef437e9cb10448b7a719e5
A383150
a(n) = Sum_{k=0..n} k^3 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "2", "18", "64", "160", "288", "224", "-1024", "-6912", "-28160", "-95744", "-294912", "-851968", "-2351104", "-6266880", "-16252928", "-41222144", "-102629376", "-251527168", "-608174080", "-1453326336", "-3437232128", "-8055160832", "-18723373056", "-43201331200", "-99019128832", "-225586446336" ]
[ "sign", "easy", "new" ]
13
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:45:24
oeisdata/seq/A383/A383150.seq
7c9c26968814be061ace0c137038934c
A383151
a(n) = Sum_{k=0..n} k^4 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "10", "36", "40", "-160", "-1152", "-4480", "-13568", "-34560", "-74240", "-123904", "-92160", "425984", "2867200", "11796480", "40763392", "128122880", "378667008", "1070858240", "2928148480", "7795113984", "20300431360", "51900317696", "130610626560", "324219699200", "795206483968", "1929715384320" ]
[ "sign", "easy", "new" ]
18
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-23T16:21:30
oeisdata/seq/A383/A383151.seq
c632c98bfd0182ec23e2989544a42ebe
A383152
a(n) = Sum_{k=0..n} k^5 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "26", "18", "-272", "-1400", "-4032", "-7168", "-1024", "55296", "294400", "1086976", "3354624", "9132032", "22249472", "47923200", "85983232", "99155968", "-102629376", "-1237712896", "-5688524800", "-20775960576", "-67868033024", "-207022456832", "-602167836672", "-1690304512000", "-4613767954432" ]
[ "sign", "easy", "new" ]
17
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T12:10:07
oeisdata/seq/A383/A383152.seq
1061d6a3a92c047ea09528855c1bf79b
A383153
Square array read by antidiagonals: A(m,n) is the number of 2m-by-2n fers-wazir tours.
[ "2", "1", "1", "1", "2", "1", "1", "4", "4", "1", "1", "9", "22", "9", "1", "1", "23", "124", "124", "23", "1", "1", "62", "818", "1620", "818", "62", "1", "1", "170", "6004", "25111", "25111", "6004", "170", "1", "1", "469", "46488", "455219", "882130", "455219", "46488", "469", "1", "1", "1297", "367880", "9103712", "36979379", "36979379", "9103712", "367880", "1297", "1" ]
[ "nonn", "tabl", "new" ]
58
1
1
[ "A339190", "A383153", "A383154" ]
null
Don Knuth, Apr 18 2025
2025-04-25T14:31:07
oeisdata/seq/A383/A383153.seq
36adfc774e55bf3eb4b6776541c6895b
A383154
The number of 2n-by-2n fers-wazir tours.
[ "2", "2", "22", "1620", "882130", "3465050546" ]
[ "nonn", "more", "new" ]
13
1
1
[ "A140519", "A383153", "A383154" ]
null
Don Knuth, Apr 18 2025
2025-04-18T13:57:51
oeisdata/seq/A383/A383154.seq
d5b6fc08e418e963cbd652185c69d2c9
A383155
a(n) = Sum_{k=0..n} k^6 * (-1)^k * 3^(n-k) * binomial(n,k).
[ "0", "-1", "58", "-180", "-1304", "-2920", "1008", "34496", "163840", "525312", "1285120", "2241536", "1124352", "-12113920", "-72052736", "-282378240", "-924581888", "-2699493376", "-7201751040", "-17666670592", "-39507722240", "-77918109696", "-121883328512", "-78622228480", "453588811776", "2904974950400", "11885785120768" ]
[ "sign", "easy", "new" ]
15
0
3
[ "A001787", "A178987", "A383150", "A383151", "A383152", "A383155" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-23T13:24:30
oeisdata/seq/A383/A383155.seq
be46b60b1d637d6eb4d74567473c5ecf
A383156
The sum of the maximum exponents in the prime factorizations of the divisors of n.
[ "0", "1", "1", "3", "1", "3", "1", "6", "3", "3", "1", "7", "1", "3", "3", "10", "1", "7", "1", "7", "3", "3", "1", "13", "3", "3", "6", "7", "1", "7", "1", "15", "3", "3", "3", "13", "1", "3", "3", "13", "1", "7", "1", "7", "7", "3", "1", "21", "3", "7", "3", "7", "1", "13", "3", "13", "3", "3", "1", "15", "1", "3", "7", "21", "3", "7", "1", "7", "3", "7", "1", "22", "1", "3", "7", "7", "3", "7", "1", "21", "10", "3", "1" ]
[ "nonn", "easy", "new" ]
10
1
4
[ "A000005", "A001221", "A001620", "A005117", "A013661", "A033150", "A034444", "A051903", "A073184", "A118914", "A252505", "A306016", "A309307", "A383156", "A383157", "A383158", "A383159" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:02
oeisdata/seq/A383/A383156.seq
9f63fb68db5f5346f96b5b85998ba4f9
A383157
a(n) is the numerator of the mean of the maximum exponents in the prime factorizations of the divisors of n.
[ "0", "1", "1", "1", "1", "3", "1", "3", "1", "3", "1", "7", "1", "3", "3", "2", "1", "7", "1", "7", "3", "3", "1", "13", "1", "3", "3", "7", "1", "7", "1", "5", "3", "3", "3", "13", "1", "3", "3", "13", "1", "7", "1", "7", "7", "3", "1", "21", "1", "7", "3", "7", "1", "13", "3", "13", "3", "3", "1", "5", "1", "3", "7", "3", "3", "7", "1", "7", "3", "7", "1", "11", "1", "3", "7", "7", "3", "7", "1", "21", "2", "3", "1", "5", "3" ]
[ "nonn", "easy", "frac", "new" ]
10
1
6
[ "A000005", "A001248", "A051903", "A118914", "A308043", "A345231", "A361062", "A383156", "A383157", "A383158" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:14
oeisdata/seq/A383/A383157.seq
448f038bf717f5aedd12186906513b37
A383158
a(n) is the denominator of the mean of the maximum exponents in the prime factorizations of the divisors of n.
[ "1", "2", "2", "1", "2", "4", "2", "2", "1", "4", "2", "6", "2", "4", "4", "1", "2", "6", "2", "6", "4", "4", "2", "8", "1", "4", "2", "6", "2", "8", "2", "2", "4", "4", "4", "9", "2", "4", "4", "8", "2", "8", "2", "6", "6", "4", "2", "10", "1", "6", "4", "6", "2", "8", "4", "8", "4", "4", "2", "4", "2", "4", "6", "1", "4", "8", "2", "6", "4", "8", "2", "6", "2", "4", "6", "6", "4", "8", "2", "10", "1", "4", "2", "4", "4", "4", "4" ]
[ "nonn", "easy", "frac", "new" ]
7
1
2
[ "A000005", "A051903", "A056798", "A118914", "A383156", "A383157", "A383158" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:39:40
oeisdata/seq/A383/A383158.seq
b785937053b5aad9edf7d7e6a4674b73
A383159
The sum of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "0", "1", "1", "2", "1", "3", "1", "3", "2", "3", "1", "5", "1", "3", "3", "4", "1", "5", "1", "5", "3", "3", "1", "7", "2", "3", "3", "5", "1", "7", "1", "5", "3", "3", "3", "6", "1", "3", "3", "7", "1", "7", "1", "5", "5", "3", "1", "9", "2", "5", "3", "5", "1", "7", "3", "7", "3", "3", "1", "11", "1", "3", "5", "6", "3", "7", "1", "5", "3", "7", "1", "8", "1", "3", "5", "5", "3", "7", "1", "9", "4", "3", "1", "11", "3", "3", "3" ]
[ "nonn", "easy", "new" ]
11
1
4
[ "A005117", "A032741", "A034444", "A051903", "A056671", "A077610", "A305611", "A325770", "A365498", "A365499", "A383156", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:40:04
oeisdata/seq/A383/A383159.seq
0c9e730c0ed1cce953b4e2e8bb5674b1
A383160
a(n) is the numerator of the mean of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "0", "1", "1", "1", "1", "3", "1", "3", "1", "3", "1", "5", "1", "3", "3", "2", "1", "5", "1", "5", "3", "3", "1", "7", "1", "3", "3", "5", "1", "7", "1", "5", "3", "3", "3", "3", "1", "3", "3", "7", "1", "7", "1", "5", "5", "3", "1", "9", "1", "5", "3", "5", "1", "7", "3", "7", "3", "3", "1", "11", "1", "3", "5", "3", "3", "7", "1", "5", "3", "7", "1", "2", "1", "3", "5", "5", "3", "7", "1", "9", "2", "3", "1", "11", "3", "3", "3" ]
[ "nonn", "easy", "frac", "new" ]
9
1
6
[ "A000961", "A001248", "A005117", "A034444", "A051903", "A077610", "A118914", "A126706", "A296082", "A345288", "A383057", "A383058", "A383157", "A383158", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:40:20
oeisdata/seq/A383/A383160.seq
3d6d9fe55a5a05d4952150a43a74af38
A383161
a(n) is the denominator of the mean of the maximum exponents in the prime factorizations of the unitary divisors of n.
[ "1", "2", "2", "1", "2", "4", "2", "2", "1", "4", "2", "4", "2", "4", "4", "1", "2", "4", "2", "4", "4", "4", "2", "4", "1", "4", "2", "4", "2", "8", "2", "2", "4", "4", "4", "2", "2", "4", "4", "4", "2", "8", "2", "4", "4", "4", "2", "4", "1", "4", "4", "4", "2", "4", "4", "4", "4", "4", "2", "8", "2", "4", "4", "1", "4", "8", "2", "4", "4", "8", "2", "1", "2", "4", "4", "4", "4", "8", "2", "4", "1", "4", "2", "8", "4", "4", "4", "4" ]
[ "nonn", "easy", "frac", "new" ]
8
1
2
[ "A034444", "A051903", "A056798", "A077610", "A118914", "A383158", "A383159", "A383160", "A383161" ]
null
Amiram Eldar, Apr 18 2025
2025-04-20T02:38:27
oeisdata/seq/A383/A383161.seq
bd12334096a94cad98b9143f4bd32410
A383163
Expansion of e.g.f. log(1 - (exp(2*x) - 1)/2)^2 / 2.
[ "0", "0", "1", "9", "75", "690", "7290", "88536", "1223628", "19019664", "328908720", "6268688448", "130615236576", "2954657491968", "72128519473920", "1890266313945600", "52937770062975744", "1577901064699594752", "49877742373556336640", "1666688195869095124992", "58704547943954039672832" ]
[ "nonn", "new" ]
12
0
4
[ "A000254", "A383149", "A383163" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:05:53
oeisdata/seq/A383/A383163.seq
c1abf99705a60bb9195b1650938bfded
A383164
Expansion of e.g.f. -log(1 - (exp(2*x) - 1)/2)^3 / 6.
[ "0", "0", "0", "1", "18", "255", "3555", "52290", "831684", "14405580", "271688580", "5562400800", "123123764808", "2933953637472", "74953425290016", "2044855241694720", "59361121229581440", "1827578437315965696", "59494057195888597248", "2042194772007257103360", "73731225467600254686720" ]
[ "nonn", "new" ]
11
0
5
[ "A000399", "A383149", "A383164", "A383166" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:10:32
oeisdata/seq/A383/A383164.seq
a73997622f9f2522b788c64e4067a2e1
A383165
Expansion of e.g.f. log(1 + (exp(2*x) - 1)/2)^2 / 2.
[ "0", "0", "1", "3", "3", "-10", "-30", "112", "588", "-2448", "-18960", "87296", "911328", "-4599296", "-61152000", "335523840", "5464904448", "-32363874304", "-627708979200", "3987441516544", "90133968949248", "-610866587369472", "-15823700431503360", "113884455221854208", "3334995367266582528", "-25385597162671308800" ]
[ "sign", "new" ]
10
0
4
[ "A009392", "A209849", "A383163", "A383165" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:46
oeisdata/seq/A383/A383165.seq
f0510b47f341ce8c08a51e577b91b52f
A383166
Expansion of e.g.f. log(1 + (exp(2*x) - 1)/2)^3 / 6.
[ "0", "0", "0", "1", "6", "15", "-15", "-210", "28", "5292", "4140", "-208560", "-369864", "11847264", "33630688", "-917280000", "-3642944640", "92903375616", "479824306944", "-11926470604800", "-76477342307840", "1892813347934208", "14591875555074048", "-363945109924577280", "-3293838565260693504", "83374884181664563200" ]
[ "sign", "new" ]
9
0
5
[ "A209849", "A383164", "A383166" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:42
oeisdata/seq/A383/A383166.seq
a9b8ba869c87f46a2c5423a7cfd36bb0
A383170
Expansion of e.g.f. -log(1 + log(1 - 2*x)/2).
[ "0", "1", "3", "16", "122", "1208", "14704", "212336", "3547984", "67337728", "1430990976", "33664165632", "868592478720", "24390846882816", "740570519159808", "24177326011834368", "844599686386919424", "31438092340685144064", "1242230898248798896128", "51933512200489564962816", "2290351520336982559358976" ]
[ "nonn", "new" ]
11
0
3
[ "A003713", "A227917", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:16:21
oeisdata/seq/A383/A383170.seq
d1dd1e6d07134eb48f4e70788739a599
A383171
Expansion of e.g.f. log(1 + log(1 - 2*x)/2)^2 / 2.
[ "0", "0", "1", "9", "91", "1090", "15298", "247352", "4537132", "93195696", "2120623984", "52973194560", "1441635171040", "42464913775232", "1346297567292416", "45715740985471744", "1655552663185480448", "63698261991541393408", "2595107348458704209920", "111613055867327344582656" ]
[ "nonn", "new" ]
11
0
4
[ "A341587", "A383163", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T10:22:17
oeisdata/seq/A383/A383171.seq
199666d43613f71ebf585fb16347362a
A383172
Expansion of e.g.f. -log(1 + log(1 - 2*x)/2)^3 / 6.
[ "0", "0", "0", "1", "18", "295", "5115", "96838", "2012724", "45825148", "1137703140", "30643915984", "891001127016", "27835772321344", "930387252759328", "33141746095999552", "1253756533365348992", "50210676392866266880", "2122613151692627299584", "94470824166941637093376" ]
[ "nonn", "new" ]
10
0
5
[ "A341588", "A383164", "A383170", "A383171", "A383172" ]
null
Seiichi Manyama, Apr 18 2025
2025-04-18T08:44:28
oeisdata/seq/A383/A383172.seq
a4177df8c5dd281840e933f98f8be9b0
A383173
Decimal expansion of the area of the biggest little decagon.
[ "7", "4", "9", "1", "3", "7", "3", "4", "5", "8", "7", "7", "8", "3", "0", "2", "7", "0", "6", "2", "2", "7", "1", "9", "8", "2", "7", "8", "8", "2", "7", "0", "1", "4", "5", "1", "9", "4", "9", "1", "5", "2", "5", "8", "0", "8", "1", "5", "0", "2", "5", "4", "5", "7", "7", "2", "1", "0", "5", "5", "3", "8", "2", "3", "2", "4", "2", "9", "2", "7", "8", "5", "6", "1", "1", "1", "9", "0", "0", "7", "7", "5", "1", "9", "8", "6", "0", "3", "7", "2", "5", "7", "6", "8", "5", "8", "6", "8", "5", "8", "7", "7", "2", "7", "5", "6", "7", "7", "8", "9", "3", "0", "8", "6", "7", "7", "6", "2", "3" ]
[ "nonn", "cons", "new" ]
7
1
1
[ "A111969", "A381252", "A383173" ]
null
Eric W. Weisstein, Apr 18 2025
2025-04-20T08:40:11
oeisdata/seq/A383/A383173.seq
3902cceab8050a4105088c7c63dba86f
A383175
Number of compositions of n such that any fixed point k can be k different colors.
[ "1", "1", "2", "5", "10", "22", "48", "101", "213", "450", "945", "1961", "4064", "8385", "17242", "35332", "72141", "146924", "298552", "605377", "1225277", "2475912", "4995754", "10067848", "20267680", "40762951", "81916919", "164504411", "330155437", "662265817", "1327860471", "2661376529", "5332341881", "10680912173" ]
[ "nonn", "easy", "new" ]
13
0
3
[ "A011782", "A088305", "A238349", "A238350", "A238351", "A335713", "A352512", "A383175" ]
null
John Tyler Rascoe, Apr 18 2025
2025-04-21T16:27:11
oeisdata/seq/A383/A383175.seq
8fea309d1fda96b8bd8298beeae4bbde
A383176
If p = A002313(n) is a prime such that p = x^2 + y^2, then a(n) is the largest integer k that satisfies x^2 + y^2 - k*x*y > 0.
[ "1", "2", "2", "4", "2", "6", "2", "3", "2", "3", "2", "2", "10", "3", "2", "3", "2", "2", "6", "2", "2", "14", "7", "2", "4", "16", "2", "2", "3", "8", "2", "2", "2", "3", "2", "2", "2", "3", "20", "6", "2", "2", "3", "5", "2", "4", "2", "2", "2", "2", "24", "3", "5", "2", "2", "6", "2", "4", "2", "26", "5", "2", "13", "3", "2", "2", "2", "2", "5", "2", "3", "2", "7", "5", "2", "2", "2", "3", "2", "7", "5", "2", "2", "3" ]
[ "nonn", "new" ]
19
1
2
[ "A002313", "A002330", "A002331", "A383176" ]
null
Gonzalo Martínez, Apr 18 2025
2025-04-27T01:12:35
oeisdata/seq/A383/A383176.seq
7383abfe9e830f5dd91dc24359d08ff3
A383190
a(2n) and a(2n+1) are the square spiral numbers of the position on which the (n+1)th domino is placed, when tiling the plane by placing the dominos always as near as possible to the origin and so that no two dominos share a long side. Inverse permutation of A383191.
[ "0", "1", "3", "4", "5", "6", "7", "22", "2", "11", "8", "9", "10", "27", "14", "13", "18", "17", "15", "16", "19", "20", "21", "44", "23", "46", "12", "29", "24", "25", "33", "34", "39", "40", "45", "76", "28", "53", "32", "31", "38", "37", "26", "51", "35", "36", "41", "42", "43", "74", "47", "78", "52", "85", "60", "59", "68", "67", "61", "62", "69", "70", "75", "114", "77", "116", "30", "55", "48", "49", "54", "87", "58", "57", "66", "65" ]
[ "nonn", "new" ]
20
0
3
[ "A174344", "A316328", "A383190", "A383191" ]
null
M. F. Hasler, Apr 18 2025
2025-04-23T10:35:15
oeisdata/seq/A383/A383190.seq
8c36f39c5cb2e770db3864c19e7348c2
A383191
a(n) is the number on the n-th position on the square spiral on the plane tiled with dominoes always placed nearest to the origin and so that no two dominos share a long side. Inverse permutation of A383190.
[ "0", "1", "8", "2", "3", "4", "5", "6", "10", "11", "12", "9", "26", "15", "14", "18", "19", "17", "16", "20", "21", "22", "7", "24", "28", "29", "42", "13", "36", "27", "66", "39", "38", "30", "31", "44", "45", "41", "40", "32", "33", "46", "47", "48", "23", "34", "25", "50", "68", "69", "76", "43", "52", "37", "70", "67", "108", "73", "72", "55", "54", "58", "59", "80", "81", "75", "74", "57", "56", "60", "61", "84", "85", "86", "49", "62" ]
[ "nonn", "new" ]
13
0
3
[ "A174344", "A316328", "A316667", "A383190", "A383191" ]
null
M. F. Hasler, Apr 18 2025
2025-04-23T10:35:36
oeisdata/seq/A383/A383191.seq
3f9b94064b18d9c2d90800da699e8261
A383196
Expansion of e.g.f. (1/(1 - 3*x)^(1/3) - 1)^3 / 6.
[ "0", "0", "0", "1", "24", "520", "11880", "295960", "8090880", "242280640", "7912262400", "280384720000", "10727852889600", "441104638374400", "19407654326860800", "910140650683264000", "45332366929833984000", "2390437704451084288000", "133060566042200788992000", "7797805996570952986624000" ]
[ "nonn", "new" ]
8
0
5
[ "A001754", "A035119", "A143169", "A371080", "A383196" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:03:38
oeisdata/seq/A383/A383196.seq
5ff144e7eabed98c0b77e4d1037584a1
A383197
Number of positive integers with n digits in which adjacent digits differ by at most 2.
[ "9", "41", "188", "867", "4010", "18574", "86096", "399225", "1851529", "8587802", "39833891", "184770640", "857073208", "3975623218", "18441391129", "85542653145", "396800342804", "1840608838251", "8537899488042", "39604141848678", "183708898915088", "852157340908409", "3952841397780937", "18335763176322738" ]
[ "nonn", "base", "easy", "new" ]
17
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-04-23T13:10:04
oeisdata/seq/A383/A383197.seq
db14b75ff51e69749e2a07f8ee8ce42f
A383198
Number of positive integers with n digits in which adjacent digits differ by at most 3.
[ "9", "54", "328", "2000", "12202", "74458", "454366", "2772710", "16920138", "103253214", "630091042", "3845059318", "23464039746", "143186649814", "873780342786", "5332145758694", "32538816680050", "198564450196598", "1211717109125762", "7394366670845606", "45123286657530514", "275359755529253142" ]
[ "nonn", "base", "easy", "new" ]
9
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-04-24T17:36:03
oeisdata/seq/A383/A383198.seq
d20750c30b94493db3e9ab707d4eca59
A383199
Number of positive integers with n digits in which adjacent digits differ by at most 4.
[ "9", "65", "475", "3465", "25282", "184463", "1345887", "9819916", "71648478", "522764591", "3814216651", "27829445433", "203050351876", "1481504383412", "10809413614854", "78868091114176", "575440631436879", "4198553757680021", "30633661742154286", "223510591001999469", "1630787227154056312" ]
[ "nonn", "base", "easy", "new" ]
11
1
1
[ "A235163", "A383197", "A383198", "A383199", "A383200", "A383201", "A383202" ]
null
Edwin Hermann, Apr 19 2025
2025-04-24T17:35:49
oeisdata/seq/A383/A383199.seq
0967cae534d0ff7d8a8c230963d0d135
A383203
Expansion of e.g.f. f(x) * exp(f(x)), where f(x) = (exp(2*x) - 1)/2.
[ "0", "1", "4", "19", "104", "641", "4380", "32803", "266768", "2337505", "21925236", "218946003", "2316939256", "25878593313", "304020964876", "3745210267939", "48248600421664", "648460085178689", "9072650530778084", "131884007007981075", "1988341404357799048", "31040812899065995073", "501049583881525932028" ]
[ "nonn", "new" ]
9
0
3
[ "A154602", "A383203" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:05:04
oeisdata/seq/A383/A383203.seq
90f43e78acefe02bf7ddbde67f06b357
A383204
Expansion of e.g.f. f(x)^2 * exp(f(x)) / 2, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "1", "9", "70", "550", "4531", "39515", "365324", "3575820", "36971461", "402741581", "4610187154", "55316069874", "694067320311", "9087012399007", "123889735839000", "1755654433460248", "25816120675972105", "393285627390135313", "6198118449550830302", "100916786871955767998", "1695424878199285059003" ]
[ "nonn", "new" ]
7
0
4
[ "A154602", "A383204" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:10
oeisdata/seq/A383/A383204.seq
dea61c70da77c30d4f1a5ead912f598c
A383205
Expansion of e.g.f. f(x)^3 * exp(f(x)) / 6, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "0", "1", "16", "190", "2080", "22491", "247072", "2792476", "32659840", "396255541", "4991365808", "65268062938", "885442472096", "12451577262671", "181326192307264", "2731564737248696", "42522062246582784", "683301050932028777", "11322975536640636240", "193300021823406703990", "3396381539718451143200" ]
[ "nonn", "new" ]
7
0
5
[ "A154602", "A383205" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:03:29
oeisdata/seq/A383/A383205.seq
b82135b49135a4bf58ab9bb9f2fd670b
A383206
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = Sum_{j=k..n} 2^(n-j) * Stirling2(n,j) * Stirling2(j,k).
[ "1", "0", "1", "0", "3", "1", "0", "11", "9", "1", "0", "49", "71", "18", "1", "0", "257", "575", "245", "30", "1", "0", "1539", "4957", "3120", "625", "45", "1", "0", "10299", "45829", "39697", "11480", "1330", "63", "1", "0", "75905", "454015", "517790", "201677", "33250", "2506", "84", "1", "0", "609441", "4804191", "6999785", "3513762", "770007", "81774", "4326", "108", "1" ]
[ "nonn", "tabl", "new" ]
11
0
5
[ "A000007", "A004211", "A130191", "A380228", "A383206", "A383207", "A383208" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:05
oeisdata/seq/A383/A383206.seq
2a5b883974d1e689b6b16d6028a27e64
A383207
Expansion of e.g.f. (exp(f(x)) - 1)^2 / 2, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "1", "9", "71", "575", "4957", "45829", "454015", "4804191", "54094749", "645720757", "8142419727", "108110708511", "1506969153757", "21993472779461", "335257957315199", "5325979566073919", "87999598425114045", "1509471498829147637", "26835040585117438415", "493677094649876461759", "9384926300821643459133" ]
[ "nonn", "new" ]
9
0
4
[ "A000558", "A383206", "A383207" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:14
oeisdata/seq/A383/A383207.seq
c26309b6d936535663680bb36987d700
A383208
Expansion of e.g.f. (exp(f(x)) - 1)^3 / 6, where f(x) = (exp(2*x) - 1)/2.
[ "0", "0", "0", "1", "18", "245", "3120", "39697", "517790", "6999785", "98520060", "1445923149", "22129416210", "352932509085", "5859167661256", "101122879922313", "1811960841148774", "33662625853200337", "647550189266734452", "12881675626292023173", "264677402162135670554", "5610552395871699336453" ]
[ "nonn", "new" ]
8
0
5
[ "A000559", "A383206", "A383208" ]
null
Seiichi Manyama, Apr 19 2025
2025-04-19T10:04:18
oeisdata/seq/A383/A383208.seq
57b73a4753c5f5f7106df4dcfa7c2254
A383209
Irregular triangle read by rows in which row n lists the odd divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such odd divisors do not exist.
[ "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "3", "0", "0", "5", "0", "0", "3", "9", "0", "5", "0", "0", "0", "3", "0", "0", "0", "7", "0", "3", "5", "15", "0", "0", "0", "0", "7", "3", "9", "0", "0", "0", "5", "0", "3", "7", "21", "0", "0", "5", "9", "15", "0", "0", "3", "0", "0", "0", "0", "0", "3", "9", "27", "0", "7", "0", "0", "0", "3", "5", "15", "0", "0", "9", "0", "0", "3", "11", "33", "0", "0", "0", "7", "0", "3", "9", "0", "0", "5", "25", "0", "11", "3", "39" ]
[ "nonn", "tabf", "new" ]
26
1
6
[ "A027750", "A237593", "A239657", "A379288", "A379374", "A379461", "A383147", "A383209" ]
null
Omar E. Pol, Apr 19 2025
2025-04-27T15:06:20
oeisdata/seq/A383/A383209.seq
bf7499be6ff27b701a0bb0257142221b
A383211
Numbers of the form p^e where p is prime and e > 1 is squarefree.
[ "4", "8", "9", "25", "27", "32", "49", "64", "121", "125", "128", "169", "243", "289", "343", "361", "529", "729", "841", "961", "1024", "1331", "1369", "1681", "1849", "2048", "2187", "2197", "2209", "2809", "3125", "3481", "3721", "4489", "4913", "5041", "5329", "6241", "6859", "6889", "7921", "8192", "9409", "10201", "10609", "11449", "11881", "12167" ]
[ "nonn", "new" ]
6
1
1
[ "A053810", "A144338", "A383211", "A383266" ]
null
Peter Luschny, Apr 21 2025
2025-04-22T02:42:59
oeisdata/seq/A383/A383211.seq
477ca3c00b28421373a164a1967b3347
A383212
a(n) = permanent of the n-th principal submatrix of the rectangular array whose odd-numbered rows are (2,1,2,1,2,1,2,1,...) and even-numbered rows are (1,2,1,2,1,2,1,2,...).
[ "1", "2", "5", "24", "132", "1032", "8820", "95616", "1106496", "15327360", "223560000", "3768768000", "66305952000", "1316927808000", "27127003680000", "620221722624000", "14638710417408000", "378633583448064000", "10073602372700160000", "290788929384726528000", "8609476463579013120000", "274361332654900592640000", "8946658680536444313600000" ]
[ "nonn", "new" ]
18
0
2
[ "A204252", "A383212" ]
null
Clark Kimberling, Apr 19 2025
2025-04-24T09:01:55
oeisdata/seq/A383/A383212.seq
ebd385abe2a7cc993a7a119e6b99610c
A383213
a(n) = number of distinct prime factors of binomial(2n,n+1).
[ "0", "1", "2", "2", "4", "3", "4", "4", "5", "5", "6", "6", "6", "7", "6", "7", "9", "8", "10", "9", "10", "10", "10", "9", "10", "10", "11", "11", "12", "13", "12", "12", "14", "14", "14", "14", "14", "14", "16", "14", "16", "15", "16", "17", "16", "17", "18", "17", "18", "18", "18", "18", "20", "18", "20", "19", "19", "20", "20", "21", "21", "21", "21", "21", "23", "22", "24", "23", "23", "23" ]
[ "nonn", "new" ]
20
1
3
[ "A000984", "A001221", "A067434", "A383213", "A383214" ]
null
Clark Kimberling, Apr 19 2025
2025-04-26T20:30:09
oeisdata/seq/A383/A383213.seq
5389de9f4d718f8164bb101c403d469d
A383215
Primes p preceded and followed by gaps whose difference (absolute value) is greater than log(p).
[ "7", "29", "31", "113", "127", "139", "149", "181", "191", "199", "223", "241", "283", "307", "317", "331", "347", "419", "421", "431", "467", "521", "523", "541", "619", "641", "661", "673", "773", "809", "811", "821", "829", "853", "863", "877", "887", "907", "953", "967", "1009", "1021", "1031", "1049", "1051", "1061", "1069", "1087", "1129", "1151", "1153", "1213", "1259", "1277" ]
[ "nonn", "new" ]
14
1
1
[ "A068985", "A383215", "A383216" ]
null
Alain Rocchelli, Apr 19 2025
2025-04-28T00:58:08
oeisdata/seq/A383/A383215.seq
7e140ea70f4a943cb2d33c4f19deae51
A383216
Primes p which are preceded and followed by gaps whose difference is greater than 2*log(p).
[ "113", "127", "523", "887", "907", "1087", "1129", "1151", "1277", "1327", "1361", "1669", "1693", "1931", "1951", "1973", "2203", "2311", "2333", "2477", "2557", "2971", "2999", "3163", "3251", "3299", "3469", "4049", "4297", "4327", "4523", "4547", "4783", "4861", "5119", "5147", "5237", "5351", "5381", "5531", "5557", "5591", "5749", "5779", "5981" ]
[ "nonn", "new" ]
11
1
1
[ "A092553", "A383215", "A383216" ]
null
Alain Rocchelli, Apr 19 2025
2025-04-26T19:39:40
oeisdata/seq/A383/A383216.seq
bd1fb16ab8199b9c94fc55368aa295d8
A383217
Lexicographically earliest strictly increasing sequence such that no term is a substring of the product of all previous terms.
[ "1", "2", "3", "4", "5", "6", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "32", "33", "34", "35", "36", "37", "40", "41", "44", "45", "46", "48", "49", "53", "54", "55", "56", "57", "59", "61", "63", "64", "65", "66", "67", "68", "69", "70", "71", "76", "79", "80", "84", "85", "87", "90", "91", "97", "98" ]
[ "nonn", "base", "new" ]
8
1
2
[ "A033180", "A383217", "A383218" ]
null
Dominic McCarty, Apr 19 2025
2025-04-19T18:07:27
oeisdata/seq/A383/A383217.seq
aa2ce0f0772886f96b3d1d59238a3d4c
A383218
The product of the first n terms of A383217.
[ "1", "2", "6", "24", "120", "720", "5760", "51840", "518400", "5702400", "68428800", "889574400", "12454041600", "186810624000", "2988969984000", "50812489728000", "914624815104000", "17377871486976000", "347557429739520000", "7298706024529920000", "160571532539658240000", "3693145248412139520000" ]
[ "nonn", "base", "new" ]
5
1
2
[ "A033180", "A383217", "A383218" ]
null
Dominic McCarty, Apr 19 2025
2025-04-19T18:07:34
oeisdata/seq/A383/A383218.seq
320642fd5e8fa7259d0287ac13f5ae1a
A383220
Integers k such that rad(k)*2^(k/rad(k)) + 1 is prime where rad = A007947.
[ "1", "2", "3", "5", "6", "11", "14", "15", "20", "21", "23", "24", "26", "29", "30", "33", "35", "39", "41", "44", "51", "53", "65", "68", "69", "74", "78", "83", "86", "88", "89", "90", "95", "105", "111", "113", "114", "116", "117", "119", "125", "126", "131", "134", "135", "138", "140", "141", "146", "147", "153", "155", "156", "158", "165", "168", "171", "173", "174", "179" ]
[ "nonn", "new" ]
8
1
2
[ "A002234", "A003557", "A005384", "A007947", "A383220" ]
null
Juri-Stepan Gerasimov, Apr 19 2025
2025-04-27T18:11:42
oeisdata/seq/A383/A383220.seq
46f26baaf604c351faa321281234eb7d
A383221
Coefficient of x^3 in expansion of (x+2) * (x+5) * ... * (x+3*n-1).
[ "0", "0", "0", "1", "26", "595", "14155", "363944", "10206700", "312193524", "10380710220", "373619597736", "14490750497432", "603032132116336", "26818416624389936", "1269883590624201344", "63806666669904903808", "3391580011320726010880", "190174443042558311293440", "11220246602286014617751040" ]
[ "nonn", "new" ]
7
0
5
[ "A225470", "A383221" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:40:40
oeisdata/seq/A383/A383221.seq
c6d3d626ae03bbfdd72830474511690b
A383222
Coefficient of x^4 in expansion of (x+2) * (x+5) * ... * (x+3*n-1).
[ "0", "0", "0", "0", "1", "40", "1275", "39655", "1276009", "43382934", "1570298610", "60630265740", "2495678898636", "109326548645600", "5085420626585936", "250576924194171120", "13046999027750243984", "716156618057417103008", "41347880768363832470304", "2505655766070932929630464" ]
[ "nonn", "new" ]
7
0
6
[ "A225470", "A383222" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:40:36
oeisdata/seq/A383/A383222.seq
e8503b36f1533fe034fb09134f2d5f08
A383223
Number of integer solutions to Product_{k=1..n} (4 + c(k)) = 4 * Product_{k=1..n} c(k) with 0 < c(k) <= c(k+1).
[ "0", "2", "15", "375", "28901", "5185573" ]
[ "nonn", "more", "new" ]
5
1
2
[ "A263207", "A375787", "A380749", "A381644", "A382672", "A383223" ]
null
Zhining Yang, Apr 19 2025
2025-04-27T05:56:54
oeisdata/seq/A383/A383223.seq
ed5f86cb83c4df86ebbc2c3af98d96a9
A383227
a(n) is the product of first n even numbers not divisible by 5 (cf. A217562)
[ "1", "2", "8", "48", "384", "4608", "64512", "1032192", "18579456", "408748032", "9809952768", "255058771968", "7141645615104", "228532659683328", "7770110429233152", "279723975452393472", "10629511067190951936", "446439464822019981312", "19643336452168879177728", "903593476799768442175488", "43372486886388885224423424" ]
[ "nonn", "new" ]
8
0
2
[ "A217562", "A356858", "A383227" ]
null
Stefano Spezia, Apr 20 2025
2025-04-21T17:05:33
oeisdata/seq/A383/A383227.seq
563e6cddff133efd665648e566220a0a
A383228
a(n) is the number of cases where both j and k (1 <= j < k <= n), are divisors of Sum_{i=j..k} i^i.
[ "0", "0", "0", "1", "1", "2", "2", "2", "3", "3", "3", "3", "3", "3", "4", "4", "5", "5", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "10", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "12", "14", "14", "14", "14", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17" ]
[ "nonn", "new" ]
20
1
6
[ "A000312", "A001923", "A128981", "A383228" ]
null
Jean-Marc Rebert, Apr 20 2025
2025-04-22T07:49:18
oeisdata/seq/A383/A383228.seq
0a3c1fec736f3d8202d0936b265e2776
A383231
Expansion of e.g.f. f(x) * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
[ "0", "1", "7", "83", "1394", "30330", "810756", "25710012", "943434288", "39324264624", "1835297984160", "94813760519136", "5371462318747392", "331125138305434368", "22065681276731119104", "1580617232453691210240", "121117633854691036502016", "9885823380533972300470272", "856279708828545483688808448" ]
[ "nonn", "new" ]
8
0
3
[ "A004041", "A024216", "A024382", "A383231", "A383232", "A383233", "A383234" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:57:13
oeisdata/seq/A383/A383231.seq
e89c953c6f09dd06448b4d169186cabc
A383232
Expansion of e.g.f. f(x)^2 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
[ "0", "1", "9", "122", "2242", "52180", "1471692", "48790608", "1859539344", "80109265824", "3849497255520", "204138860091264", "11842095171021696", "745962168915065088", "50708105952635996928", "3699802551156676392960", "288399758863879774476288", "23919432333548949807869952", "2103184085769044913951461376" ]
[ "nonn", "new" ]
8
0
3
[ "A383231", "A383232", "A383233", "A383234" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:57:09
oeisdata/seq/A383/A383232.seq
6241beba3ecb939b393ddb7e987560b0
A383233
Expansion of e.g.f. f(x)^3 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
[ "0", "1", "11", "167", "3318", "81930", "2423208", "83582568", "3295488816", "146241365904", "7214605476480", "391735046081664", "23216763331632384", "1491431668108800768", "103230214859003968512", "7659080261784464808960", "606407304545822037952512", "51033731719180664212641792", "4549228202963725560906891264" ]
[ "nonn", "new" ]
13
0
3
[ "A383231", "A383232", "A383233", "A383234" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T10:39:38
oeisdata/seq/A383/A383233.seq
467038ecaa06b02f2849739ad5ec11d8
A383234
Expansion of e.g.f. f(x)^4 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
[ "0", "1", "13", "218", "4646", "121080", "3741144", "133863792", "5447294352", "248518603584", "12566268267840", "697632464382336", "42189230206182528", "2760816706845539328", "194381535085933095936", "14652311175996819978240", "1177370323796943823325184", "100466288729505689717809152" ]
[ "nonn", "new" ]
7
0
3
[ "A383231", "A383232", "A383233", "A383234" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:40:53
oeisdata/seq/A383/A383234.seq
7107bef1eabbcadc835482d59c33ce22
A383235
Triangle read by rows: T(n,k) = 2*floor(k/2)*T(n-1,k) + T(n-1,k-1), 0 <= k <= n.
[ "1", "0", "1", "0", "0", "1", "0", "0", "2", "1", "0", "0", "4", "4", "1", "0", "0", "8", "12", "8", "1", "0", "0", "16", "32", "44", "12", "1", "0", "0", "32", "80", "208", "92", "18", "1", "0", "0", "64", "192", "912", "576", "200", "24", "1", "0", "0", "128", "448", "3840", "3216", "1776", "344", "32", "1", "0", "0", "256", "1024", "15808", "16704", "13872", "3840", "600", "40", "1" ]
[ "nonn", "tabl", "new" ]
12
0
9
[ "A000079", "A001787", "A007472", "A007590", "A048993", "A100575", "A158681", "A383235" ]
null
Ven Popov, Apr 20 2025.
2025-04-24T13:26:59
oeisdata/seq/A383/A383235.seq
c4f2641c84f06bab672053ffc3a43041
A383236
The least number of applications of Ackermann-Péter functions to reach n, starting from 0.
[ "1", "2", "3", "4", "4", "5", "5", "6", "6", "7", "7", "8", "5", "6", "7", "8", "8", "9", "9", "10", "9", "10", "10", "11", "10", "11", "11", "12", "6", "7", "8", "9", "10", "11", "11", "12", "11", "12", "12", "13", "12", "13", "13", "14", "12", "13", "13", "14", "13", "14", "14", "15", "13", "14", "14", "15", "14", "15", "15", "16", "7", "8", "9", "10" ]
[ "nonn", "look", "new" ]
20
1
2
[ "A143796", "A368423", "A383236" ]
null
Hendrik Ballhausen, Apr 20 2025
2025-04-24T13:34:55
oeisdata/seq/A383/A383236.seq
302999f7dff310f03b7ef61c8005e50a
A383237
Primes p such that x^5+x+1 has no roots modulo p.
[ "2", "29", "41", "47", "71", "131", "179", "197", "233", "239", "257", "269", "311", "353", "443", "461", "491", "509", "587", "647", "653", "683", "761", "857", "863", "887", "929", "947", "1013", "1061", "1223", "1277", "1283", "1289", "1301", "1361", "1373", "1409", "1427", "1439", "1499", "1511", "1559", "1619", "1637", "1733", "1823", "1973", "1979" ]
[ "nonn", "new" ]
11
1
1
[ "A003627", "A383237" ]
null
Jayde S. Massmann, Apr 20 2025
2025-04-24T13:22:49
oeisdata/seq/A383/A383237.seq
cca30d3fde094657d68247a5fd870943
A383255
Number of n X n {0,1,2,3} matrices having no 1's to the right of any 0's and no 3's above any 2's.
[ "1", "4", "194", "107080", "672498596", "48104236145168", "39202958861329453384", "364022757339778569993689888", "38513979937284562006371342202842000", "46429021191757554279412904483559912259714112", "637737721080296383894709847744103523361428384973270816" ]
[ "nonn", "new" ]
13
0
2
[ "A002416", "A006506", "A014235", "A060757", "A181213", "A213977", "A381857", "A383255" ]
null
John Tyler Rascoe, Apr 20 2025
2025-04-23T14:57:45
oeisdata/seq/A383/A383255.seq
3562c878bc234934c9845c610a7097b0
A383256
Number of n X n matrices of nonnegative entries with all columns summing to n and no horizontally adjacent zeros.
[ "1", "1", "7", "343", "125465", "366908001", "8698468668251", "1708834003295306868", "2810884261025802145414705", "39088555382409783097546399456477", "4626844513673581956954679383115038810744", "4688191496359773864437279635019555242588548880831" ]
[ "nonn", "new" ]
10
0
3
[ "A008300", "A120733", "A145839", "A261780", "A382923", "A383256" ]
null
John Tyler Rascoe, Apr 21 2025
2025-04-23T17:02:34
oeisdata/seq/A383/A383256.seq
41ca71d0c44fc52446a4e63aee51386d
A383258
LCM-transform of A064664 (the inverse of the EKG-sequence).
[ "1", "2", "5", "3", "1", "2", "7", "2", "1", "3", "1", "1", "1", "13", "11", "17", "1", "1", "37", "1", "1", "19", "43", "2", "1", "3", "1", "1", "1", "23", "61", "31", "1", "2", "5", "1", "67", "1", "29", "1", "1", "1", "3", "41", "1", "1", "89", "1", "1", "1", "1", "47", "1", "1", "53", "7", "1", "1", "107", "1", "1", "1", "1", "2", "1", "59", "2", "1", "1", "1", "1", "1", "1", "1", "1", "71", "1", "1", "151", "1", "1", "73", "1", "1", "1", "1", "1", "79", "167", "83", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "197" ]
[ "nonn", "new" ]
14
1
2
[ "A064413", "A064664", "A064954", "A265576", "A368900", "A383258" ]
null
Antti Karttunen, Apr 21 2025
2025-04-21T11:15:51
oeisdata/seq/A383/A383258.seq
39d33e0ac6da2b58fcfa0f656e2fea63
A383259
a(n) is the excess of even composites over odd composites in the first n positive integers.
[ "0", "0", "0", "1", "1", "2", "2", "3", "2", "3", "3", "4", "4", "5", "4", "5", "5", "6", "6", "7", "6", "7", "7", "8", "7", "8", "7", "8", "8", "9", "9", "10", "9", "10", "9", "10", "10", "11", "10", "11", "11", "12", "12", "13", "12", "13", "13", "14", "13", "14", "13", "14", "14", "15", "14", "15", "14", "15", "15", "16", "16", "17", "16", "17", "16", "17", "17", "18", "17", "18", "18", "19", "19", "20" ]
[ "nonn", "easy", "new" ]
13
1
6
[ "A000034", "A000720", "A002808", "A066247", "A071904", "A383037", "A383259" ]
null
Felix Huber, Apr 24 2025
2025-04-25T20:38:05
oeisdata/seq/A383/A383259.seq
d68d5cbfbf6b4c0b93faf8e7b2f8434e
A383260
Expansion of e.g.f. f(x) * exp(f(x)), where f(x) = (exp(3*x) - 1)/3.
[ "0", "1", "5", "30", "211", "1691", "15126", "148975", "1599401", "18563832", "231317677", "3076301471", "43448641176", "648950825173", "10212710942609", "168797691270438", "2921824286030527", "52833169082034839", "995732022426733782", "19519908917429511307", "397294691005861642805", "8381466690394292755896" ]
[ "nonn", "new" ]
13
0
3
[ "A024216", "A138378", "A383203", "A383260", "A383261", "A383262" ]
null
Seiichi Manyama, Apr 21 2025
2025-04-21T09:53:11
oeisdata/seq/A383/A383260.seq
70c47c38cb39c1192f988f4c70b770f4
A383261
Expansion of e.g.f. f(x) * exp(2 * f(x)), where f(x) = (exp(3*x) - 1)/3.
[ "0", "1", "7", "57", "527", "5441", "61959", "770281", "10364671", "149854545", "2313932471", "37963374329", "658873048623", "12050610195937", "231496456566631", "4657345160220681", "97873704021590111", "2143496712532350833", "48821033290172899095", "1154261436241093805593", "28279753601438144211343" ]
[ "nonn", "new" ]
9
0
3
[ "A024395", "A383260", "A383261" ]
null
Seiichi Manyama, Apr 21 2025
2025-04-21T09:54:00
oeisdata/seq/A383/A383261.seq
a08f460c8b0fbab071b00a663fa891a3
A383262
Expansion of e.g.f. f(x)^2 * exp(f(x)) / 2, where f(x) = (exp(3*x) - 1)/3.
[ "0", "0", "1", "12", "123", "1270", "13776", "158718", "1944685", "25294338", "348340491", "5064749074", "77528735868", "1246096312188", "20976610875949", "368984700979440", "6767792258171547", "129182459141936566", "2561529454871582772", "52676675861728386114", "1121762199908797394977" ]
[ "nonn", "new" ]
11
0
4
[ "A003128", "A286721", "A383204", "A383262" ]
null
Seiichi Manyama, Apr 21 2025
2025-04-21T09:55:09
oeisdata/seq/A383/A383262.seq
f4d2993b16891d1dae25aaf7d8fb36fb
A383263
Union of prime powers (A246655) and numbers that are not squarefree (A013929).
[ "2", "3", "4", "5", "7", "8", "9", "11", "12", "13", "16", "17", "18", "19", "20", "23", "24", "25", "27", "28", "29", "31", "32", "36", "37", "40", "41", "43", "44", "45", "47", "48", "49", "50", "52", "53", "54", "56", "59", "60", "61", "63", "64", "67", "68", "71", "72", "73", "75", "76", "79", "80", "81", "83", "84", "88", "89", "90", "92", "96", "97", "98", "99", "100", "101", "103" ]
[ "nonn", "new" ]
8
1
1
[ "A013929", "A246655", "A363597", "A383263" ]
null
Peter Luschny, Apr 27 2025
2025-04-27T15:02:20
oeisdata/seq/A383/A383263.seq
dd6b8c0bd7633a871b3caaaf67b7c175
A383264
Numbers whose vSPD is not squarefree, where vSPD(n) is the valuation of the smallest prime divisor for n >= 2.
[ "16", "48", "80", "81", "112", "144", "176", "208", "240", "256", "272", "304", "336", "368", "400", "405", "432", "464", "496", "512", "528", "560", "567", "592", "624", "625", "656", "688", "720", "752", "768", "784", "816", "848", "880", "891", "912", "944", "976", "1008", "1040", "1053", "1072", "1104", "1136", "1168", "1200", "1232", "1264", "1280", "1296" ]
[ "nonn", "easy", "new" ]
22
1
1
[ "A008683", "A013929", "A067029", "A383264" ]
null
Peter Luschny, Apr 25 2025
2025-04-26T08:27:53
oeisdata/seq/A383/A383264.seq
83e01d31e95306b0a643e972404c5894
A383265
a(n) = Sum_{k=0..n} A383266(n, k).
[ "0", "2", "7", "14", "24", "35", "48", "63", "81", "101", "122", "145", "170", "197", "226", "257", "292", "327", "364", "403", "444", "487", "532", "579", "628", "680", "733", "789", "846", "905", "966", "1029", "1095", "1162", "1231", "1302", "1376", "1451", "1528", "1607", "1688", "1771", "1856", "1943", "2032", "2123", "2216", "2311", "2408", "2508", "2609" ]
[ "nonn", "new" ]
5
0
2
[ "A383265", "A383266" ]
null
Peter Luschny, Apr 21 2025
2025-04-21T16:04:25
oeisdata/seq/A383/A383265.seq
0f018042c024fdaf911dffc386b5fb40
A383266
Triangle read by rows: For n, k >= 2 T(n, k) is defined as the exponent of the highest power e of k such that k^e <= n. Otherwise T(n, 0) = n^2 and T(n, 1) = n.
[ "0", "1", "1", "4", "2", "1", "9", "3", "1", "1", "16", "4", "2", "1", "1", "25", "5", "2", "1", "1", "1", "36", "6", "2", "1", "1", "1", "1", "49", "7", "2", "1", "1", "1", "1", "1", "64", "8", "3", "1", "1", "1", "1", "1", "1", "81", "9", "3", "2", "1", "1", "1", "1", "1", "1", "100", "10", "3", "2", "1", "1", "1", "1", "1", "1", "1", "121", "11", "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "144", "12", "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabl", "new" ]
7
0
4
[ "A000196", "A383265", "A383266" ]
null
Peter Luschny, Apr 21 2025
2025-04-21T17:08:49
oeisdata/seq/A383/A383266.seq
e6412498774c23d0766334fdb4156935
A383271
Number of primes (excluding n) that may be generated by replacing any binary digit of n with a digit from 0 to 1.
[ "0", "0", "1", "1", "1", "1", "2", "2", "0", "2", "2", "1", "1", "1", "0", "3", "1", "1", "2", "3", "0", "4", "1", "3", "0", "2", "0", "3", "1", "2", "1", "2", "0", "2", "1", "2", "1", "2", "0", "3", "1", "1", "1", "4", "0", "5", "1", "1", "0", "2", "0", "2", "1", "2", "0", "2", "0", "3", "1", "1", "1", "2", "0", "4", "0", "3", "2", "3", "0", "3", "1", "4", "1", "1", "0", "5", "0", "4", "1", "1", "0", "4", "1", "2", "0", "0", "0", "3", "1", "1" ]
[ "nonn", "base", "new" ]
27
0
7
[ "A070939", "A145667", "A209252", "A352942", "A383271" ]
null
Michael S. Branicky, Apr 21 2025
2025-04-23T19:31:05
oeisdata/seq/A383/A383271.seq
90af0b86eb34029de4e2dd474e7d824f
A383272
Positions of records in A383271.
[ "0", "2", "6", "15", "21", "45", "111", "261", "1605", "1995", "4935", "8295", "69825", "268155", "550725", "4574955", "12024855", "39867135", "398467245", "1698754365", "16351800465" ]
[ "nonn", "base", "new" ]
19
1
2
[ "A276694", "A322743", "A383271", "A383272" ]
null
Michael S. Branicky, Apr 21 2025
2025-04-23T02:38:52
oeisdata/seq/A383/A383272.seq
bdbfebccceb4887776cd21e2aa932ca1
A383274
a(n) = Sum_{i,j = 0..n} C(n, i)^2*C(n, j)^2*C(i+j, i)*2^(i+j).
[ "1", "13", "441", "20629", "1119361", "66116013", "4126228569", "267666251733", "17868312820737", "1219477111897933", "84701899713767161", "5967906378862013973", "425503428034568158081", "30642774518964618986989", "2225692868157573335052441", "162858794856607965831417429", "11993850186156155815298686977" ]
[ "nonn", "new" ]
32
0
2
[ "A005259", "A383274" ]
null
Zhi-Wei Sun, Apr 26 2025
2025-04-27T11:27:14
oeisdata/seq/A383/A383274.seq
56a47e654723c32da7e17c6140f826e0
A383275
Number of compositions of n such that any part 1 can be k different colors where k is the current record having appeared in the composition.
[ "1", "1", "2", "5", "14", "42", "134", "454", "1634", "6245", "25321", "108779", "494443", "2374288", "12024257", "64100444", "358948674", "2106756217", "12931155910", "82823317389", "552400947902", "3829070637080", "27534807426150", "205066734143893", "1579309451332366", "12559941159979791", "103013928588389695" ]
[ "nonn", "easy", "new" ]
12
0
3
[ "A000108", "A011782", "A088305", "A382312", "A382991", "A383101", "A383175", "A383275" ]
null
John Tyler Rascoe, Apr 21 2025
2025-04-24T09:39:13
oeisdata/seq/A383/A383275.seq
167b6a068c4654dc99287a2d568d2a3e
A383276
Numbers of the form A034444(k) * k.
[ "1", "4", "6", "8", "10", "14", "16", "18", "22", "24", "26", "32", "34", "38", "40", "46", "48", "50", "54", "56", "58", "60", "62", "64", "72", "74", "80", "82", "84", "86", "88", "94", "96", "98", "104", "106", "112", "118", "122", "128", "132", "134", "136", "140", "142", "144", "146", "152", "156", "158", "160", "162", "166", "176", "178", "180", "184", "192", "194", "200" ]
[ "nonn", "easy", "new" ]
12
1
2
[ "A005087", "A007814", "A034444", "A036438", "A100484", "A138929", "A151821", "A298473", "A383276", "A383277", "A383278", "A383279" ]
null
Amiram Eldar, Apr 21 2025
2025-04-26T03:33:22
oeisdata/seq/A383/A383276.seq
9efed28e953519d4453e9c35af06efa4
A383277
The number of divisors d of n for which A034444(d)*d is equal to n.
[ "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn", "easy", "new" ]
7
1
null
[ "A005087", "A007814", "A034444", "A327166", "A383276", "A383277", "A383278", "A383279" ]
null
Amiram Eldar, Apr 21 2025
2025-04-22T02:46:10
oeisdata/seq/A383/A383277.seq
b2b1d8c25f9d78827dcc50cfeed78add
A383278
The number of integers k such that A034444(k) * k <= n.
[ "1", "1", "1", "2", "2", "3", "3", "4", "4", "5", "5", "5", "5", "6", "6", "7", "7", "8", "8", "8", "8", "9", "9", "10", "10", "11", "11", "11", "11", "11", "11", "12", "12", "13", "13", "13", "13", "14", "14", "15", "15", "15", "15", "15", "15", "16", "16", "17", "17", "18", "18", "18", "18", "19", "19", "20", "20", "21", "21", "22", "22", "23", "23", "24", "24", "24", "24", "24", "24", "24", "24" ]
[ "nonn", "easy", "new" ]
11
1
4
[ "A034444", "A087197", "A345288", "A356005", "A383276", "A383277", "A383278", "A383279" ]
null
Amiram Eldar, Apr 21 2025
2025-04-22T02:47:18
oeisdata/seq/A383/A383278.seq
fa7eb3f5290cbd13d780bbae99e9b2dd
A383279
The unique solution to x * A034444(x) = A383276(n).
[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "6", "13", "16", "17", "19", "10", "23", "12", "25", "27", "14", "29", "15", "31", "32", "18", "37", "20", "41", "21", "43", "22", "47", "24", "49", "26", "53", "28", "59", "61", "64", "33", "67", "34", "35", "71", "36", "73", "38", "39", "79", "40", "81", "83", "44", "89", "45", "46", "48", "97", "50", "101", "51", "103", "52", "107", "54", "109" ]
[ "nonn", "easy", "new" ]
10
1
2
[ "A000265", "A005087", "A007814", "A034444", "A383276", "A383277", "A383278", "A383279" ]
null
Amiram Eldar, Apr 21 2025
2025-04-22T02:43:27
oeisdata/seq/A383/A383279.seq
5f1e908aab5e6cf92da2d08906d584e3
A383280
a(n) = (3/2)^n * Sum_{k=0..n} (1/6)^k * (2*k)! * (n-k)! * binomial(n,k)^2.
[ "1", "2", "9", "72", "954", "19980", "624510", "27420120", "1607036760", "120942324720", "11351106055800", "1298791163577600", "177888712528573200", "28728740092874421600", "5401708378739722249200", "1169716267087957140552000", "288993599402729842084464000", "80796133625685147464322528000" ]
[ "nonn", "new" ]
15
0
2
[ "A000681", "A001499", "A383280" ]
null
Seiichi Manyama, Apr 22 2025
2025-04-24T04:22:44
oeisdata/seq/A383/A383280.seq
79ee57fee2b899e39d385d945db6bba6
A383281
a(n) = Sum_{k=0..n} (2*k+1) * (1/2)^(n+k) * (2*k)! * (n-k)! * binomial(n,k)^2.
[ "1", "2", "11", "120", "2202", "61260", "2407770", "127116360", "8680455000", "744631438320", "78393873940200", "9938444069030400", "1493483322288157200", "262511581007832156000", "53360641241377862792400", "12420661873849173800856000", "3282370875452495120806512000", "977378127650967704776130016000" ]
[ "nonn", "new" ]
16
0
2
[ "A002018", "A383281" ]
null
Seiichi Manyama, Apr 22 2025
2025-04-24T04:34:28
oeisdata/seq/A383/A383281.seq
2fe6871b660170469a02255d806853fd
A383282
a(n) = Sum_{k=0..n} (2*k+1) * (-1/2)^(n+k) * (2*k)! * (n-k)! * binomial(n,k)^2.
[ "1", "1", "5", "51", "906", "24690", "956790", "49993650", "3387124440", "288755250840", "30247310482200", "3818739956308200", "571858101118458000", "100218359688123877200", "20319306632495415745200", "4719164981053010642154000", "1244680987088062472732784000", "369981708267221405777101680000" ]
[ "nonn", "new" ]
13
0
3
[ "A383281", "A383282" ]
null
Seiichi Manyama, Apr 22 2025
2025-04-24T04:37:56
oeisdata/seq/A383/A383282.seq
49323e257bc53f5d253e10a3dc7569f7
A383284
Lexicographically earliest infinite sequence such that a(i) = a(j) => A265576(i) = A265576(j), for all i, j >= 1, where A265576 is the LCM-transform of EKG-sequence.
[ "1", "2", "2", "3", "1", "3", "1", "2", "4", "1", "1", "1", "5", "1", "1", "1", "2", "1", "6", "1", "1", "3", "1", "4", "1", "1", "7", "1", "1", "1", "2", "8", "1", "1", "1", "9", "1", "1", "1", "1", "1", "10", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "11", "1", "1", "1", "12", "1", "1", "1", "2", "1", "13", "1", "1", "1", "1", "1", "1", "14", "1", "1", "3", "1", "1", "1", "15", "1", "1", "1", "1", "1", "1", "1", "16", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "17" ]
[ "nonn", "new" ]
12
1
2
[ "A000720", "A064413", "A064423", "A265576", "A383284", "A383285" ]
null
Antti Karttunen, Apr 22 2025
2025-04-22T09:09:42
oeisdata/seq/A383/A383284.seq
55d55dea9ff85006f967d55106b58063
A383285
Positions of terms > 1 in A265576, where A265576 is the LCM-transform of EKG-sequence.
[ "2", "3", "4", "6", "8", "9", "13", "17", "19", "22", "24", "27", "31", "32", "36", "42", "50", "56", "60", "64", "66", "73", "76", "80", "88", "99", "106", "112", "114", "122", "124", "127", "133", "137", "150", "159", "166", "171", "181", "188", "196", "202", "206", "215", "232", "235", "240", "252", "258", "263", "278", "286", "290", "296", "304", "313", "319", "327", "335", "343", "359", "362", "370", "376", "380", "400", "419", "429", "437", "443" ]
[ "nonn", "new" ]
10
1
1
[ "A064413", "A064423", "A265576", "A383284", "A383285", "A383295" ]
null
Antti Karttunen, Apr 22 2025
2025-04-22T15:26:27
oeisdata/seq/A383/A383285.seq
b3879e39a842ff950c8c898a209a2df4
A383292
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(2*s) + 1/p^(3*s)).
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "3", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "3", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "3", "3", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "2", "1", "1", "1", "3", "1", "2", "2", "4" ]
[ "nonn", "mult", "easy", "new" ]
18
1
4
[ "A001694", "A046100", "A073184", "A095691", "A330595", "A365498", "A365552", "A368105", "A380922", "A383292" ]
null
Vaclav Kotesovec, Apr 22 2025
2025-04-22T14:17:11
oeisdata/seq/A383/A383292.seq
c26a2c15ef62306e5801aac6653f3114
A383293
Exponential of Mangoldt function applied to EKG-sequence: a(n) = A014963(A064413(n)).
[ "1", "2", "2", "1", "3", "3", "1", "2", "1", "5", "1", "1", "1", "7", "1", "1", "2", "1", "1", "11", "1", "3", "1", "5", "1", "1", "1", "13", "1", "1", "2", "1", "17", "1", "1", "1", "19", "1", "1", "1", "1", "1", "23", "1", "1", "1", "1", "1", "1", "7", "1", "1", "1", "1", "1", "1", "29", "1", "1", "1", "31", "1", "1", "2", "1", "1", "37", "1", "1", "1", "1", "1", "1", "41", "1", "3", "1", "1", "1", "1", "43", "1", "1", "1", "1", "1", "1", "1", "47", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "53" ]
[ "nonn", "new" ]
7
1
2
[ "A014963", "A064413", "A265576", "A383293", "A383294" ]
null
Antti Karttunen, Apr 22 2025
2025-04-22T13:33:23
oeisdata/seq/A383/A383293.seq
9c6eeb49dc6f74eec39a39244533aa09