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int64
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2.35k
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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-14 02:38:35
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A382416
Numbers with at least one zero in their base-6 representation.
[ "0", "6", "12", "18", "24", "30", "36", "37", "38", "39", "40", "41", "42", "48", "54", "60", "66", "72", "73", "74", "75", "76", "77", "78", "84", "90", "96", "102", "108", "109", "110", "111", "112", "113", "114", "120", "126", "132", "138", "144", "145", "146", "147", "148", "149", "150", "156", "162", "168", "174", "180", "181", "182", "183", "184", "185", "186", "192", "198" ]
[ "nonn", "base", "easy" ]
6
1
2
[ "A007092", "A011540", "A043369", "A062289", "A081605", "A196032", "A248910", "A382413", "A382415", "A382416", "A382417", "A382418" ]
null
Paolo Xausa, Mar 25 2025
2025-03-26T21:49:11
oeisdata/seq/A382/A382416.seq
44bfa9f93756b8a2ec9ba6eac2e4e758
A382417
Numbers with at least one zero in their base-8 representation.
[ "0", "8", "16", "24", "32", "40", "48", "56", "64", "65", "66", "67", "68", "69", "70", "71", "72", "80", "88", "96", "104", "112", "120", "128", "129", "130", "131", "132", "133", "134", "135", "136", "144", "152", "160", "168", "176", "184", "192", "193", "194", "195", "196", "197", "198", "199", "200", "208", "216", "224", "232", "240", "248", "256", "257", "258", "259", "260" ]
[ "nonn", "base", "easy" ]
6
1
2
[ "A007094", "A011540", "A043421", "A062289", "A081605", "A196032", "A255805", "A382413", "A382415", "A382416", "A382417", "A382418" ]
null
Paolo Xausa, Mar 25 2025
2025-03-26T21:49:20
oeisdata/seq/A382/A382417.seq
6cf1b4c19a2d340e043f697e044cb15b
A382418
Numbers with at least one zero in their base-9 representation.
[ "0", "9", "18", "27", "36", "45", "54", "63", "72", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90", "99", "108", "117", "126", "135", "144", "153", "162", "163", "164", "165", "166", "167", "168", "169", "170", "171", "180", "189", "198", "207", "216", "225", "234", "243", "244", "245", "246", "247", "248", "249", "250", "251", "252", "261", "270", "279", "288", "297" ]
[ "nonn", "base", "easy" ]
6
1
2
[ "A007095", "A011540", "A043453", "A062289", "A081605", "A196032", "A255808", "A382413", "A382415", "A382416", "A382417", "A382418" ]
null
Paolo Xausa, Mar 25 2025
2025-03-26T21:49:27
oeisdata/seq/A382/A382418.seq
b1ed4ece688a64be3b966d3e761f0e28
A382419
The product of exponents in the prime factorization of the cubefree numbers.
[ "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "2", "4", "1", "1" ]
[ "nonn", "easy" ]
9
1
4
[ "A002117", "A004709", "A005361", "A330594", "A368712", "A376366", "A382419", "A382421", "A382422" ]
null
Amiram Eldar, Mar 25 2025
2025-03-25T10:11:40
oeisdata/seq/A382/A382419.seq
309877ce3f390f854f768261bf5f554f
A382420
The number of non-unitary prime divisors of the noncubefree numbers.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1" ]
[ "nonn", "easy" ]
7
1
11
[ "A002117", "A046099", "A085548", "A376366", "A382420" ]
null
Amiram Eldar, Mar 25 2025
2025-03-25T08:55:53
oeisdata/seq/A382/A382420.seq
27fd7c8fd575f7b665c6e29603f7b7d8
A382421
The product of exponents in the prime factorization of the noncubefree numbers.
[ "3", "4", "3", "3", "5", "3", "4", "3", "3", "6", "6", "4", "4", "3", "5", "3", "6", "4", "3", "3", "7", "3", "3", "8", "3", "5", "4", "3", "4", "3", "3", "6", "6", "4", "9", "5", "3", "4", "5", "3", "3", "8", "3", "3", "4", "3", "10", "3", "3", "4", "3", "6", "8", "3", "4", "3", "3", "3", "5", "6", "4", "3", "3", "3", "7", "6", "8", "4", "3", "5", "3", "12", "3", "6", "3", "3", "4", "3", "5", "5", "3", "4", "6", "6", "9", "3", "3" ]
[ "nonn", "easy" ]
7
1
1
[ "A002117", "A005361", "A013661", "A013664", "A046099", "A082695", "A330594", "A368039", "A382419", "A382421" ]
null
Amiram Eldar, Mar 25 2025
2025-03-25T10:11:45
oeisdata/seq/A382/A382421.seq
523426702ac727a8840def7b90112808
A382422
The product of exponents in the prime factorization of the biquadratefree numbers.
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "2", "1" ]
[ "nonn", "easy" ]
8
1
4
[ "A003586", "A005361", "A013662", "A046100", "A082695", "A375766", "A375768", "A382422", "A382423", "A382424" ]
null
Amiram Eldar, Mar 25 2025
2025-03-25T10:11:51
oeisdata/seq/A382/A382422.seq
6ac227a54b36f5521ff4dbb6207d5e7e
A382423
The number of exponents in the prime factorization of n-th biquadratefree number that are equal to 2.
[ "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0" ]
[ "nonn", "easy" ]
11
1
34
[ "A013662", "A046100", "A369427", "A376366", "A382422", "A382423", "A382424", "A382425" ]
null
Amiram Eldar, Mar 25 2025
2025-03-26T11:38:24
oeisdata/seq/A382/A382423.seq
8fbb93b788c080304b8ccf3bf5f72a4c
A382424
The number of exponents in the prime factorization of n-th biquadratefree number that are equal to 3.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn", "easy" ]
12
1
null
[ "A013662", "A046100", "A295883", "A376366", "A382422", "A382423", "A382424", "A382425" ]
null
Amiram Eldar, Mar 25 2025
2025-03-26T11:38:29
oeisdata/seq/A382/A382424.seq
cd5a0048db4f5dd1e6756393ad3ae3a8
A382425
The number of non-unitary prime divisors of the biquadratefree numbers.
[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "2", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0" ]
[ "nonn", "easy" ]
12
1
34
[ "A013662", "A046100", "A056170", "A376366", "A382422", "A382423", "A382424", "A382425" ]
null
Amiram Eldar, Mar 25 2025
2025-03-25T08:55:36
oeisdata/seq/A382/A382425.seq
4851237a1c6933679a90ae8523b96077
A382426
MM-numbers of sets of constant multisets with distinct sums.
[ "1", "2", "3", "5", "6", "7", "10", "11", "14", "15", "17", "19", "21", "22", "23", "30", "31", "33", "34", "38", "41", "42", "46", "51", "53", "55", "57", "59", "62", "66", "67", "69", "77", "82", "83", "85", "93", "95", "97", "102", "103", "106", "109", "110", "114", "115", "118", "119", "123", "127", "131", "133", "134", "138", "154", "155", "157", "159", "161", "165", "166" ]
[ "nonn" ]
8
1
2
[ "A000688", "A000720", "A000961", "A055396", "A056239", "A061395", "A112798", "A279786", "A302242", "A302492", "A302494", "A321469", "A326534", "A326535", "A355743", "A356065", "A381635", "A381636", "A381716", "A382201", "A382203", "A382215", "A382304", "A382426" ]
null
Gus Wiseman, Apr 01 2025
2025-04-03T14:57:53
oeisdata/seq/A382/A382426.seq
f65669b3f85f2f4f2a647772cbd7600d
A382427
Number of integer partitions of n that can be partitioned into constant blocks with distinct sums.
[ "1", "1", "2", "3", "4", "7", "11", "14", "19", "28", "39", "50", "70", "91", "120", "161", "203", "260", "338", "426", "556", "695", "863", "1082", "1360", "1685" ]
[ "nonn", "more" ]
13
0
3
[ "A000009", "A000041", "A000688", "A001055", "A006171", "A045778", "A047966", "A050361", "A265947", "A279784", "A279786", "A295935", "A300383", "A300385", "A317141", "A326535", "A353864", "A355743", "A381453", "A381455", "A381633", "A381635", "A381636", "A381716", "A381717", "A381718", "A381990", "A381991", "A381992", "A381993", "A382075", "A382079", "A382203", "A382301", "A382427", "A382876" ]
null
Gus Wiseman, Mar 26 2025
2025-04-27T09:09:21
oeisdata/seq/A382/A382427.seq
94ca33da9d145fb64d9aa4da0394547c
A382428
Number of normal multiset partitions of weight n into sets with distinct sizes.
[ "1", "1", "1", "6", "8", "35", "292", "673", "2818", "16956", "219772", "636748", "3768505", "20309534", "183403268", "3227600747", "12272598308", "81353466578", "561187259734", "4416808925866", "50303004612136", "1238783066956740", "5566249468690291", "44970939483601100", "330144217684933896", "3131452652308459402" ]
[ "nonn" ]
14
0
4
[ "A000110", "A000670", "A001055", "A007716", "A019536", "A034691", "A035310", "A045778", "A050320", "A050326", "A055932", "A089259", "A116539", "A116540", "A255903", "A255906", "A270995", "A275780", "A279785", "A296119", "A317532", "A318360", "A326517", "A326518", "A326519", "A331638", "A333217", "A358830", "A381633", "A381718", "A382214", "A382216", "A382428", "A382429" ]
null
Gus Wiseman, Mar 29 2025
2025-03-31T13:38:47
oeisdata/seq/A382/A382428.seq
3108d26568937e60d4ebf42c2a4e2a87
A382429
Number of normal multiset partitions of weight n into sets with a common sum.
[ "1", "1", "2", "3", "5", "7", "13", "26", "57", "113", "283", "854", "2401", "6998", "24072", "85061", "308956", "1190518", "4770078", "19949106", "87059592" ]
[ "nonn", "more" ]
17
0
3
[ "A000110", "A000670", "A001055", "A019536", "A034691", "A035310", "A038041", "A045778", "A050320", "A055932", "A089259", "A116539", "A116540", "A255903", "A255906", "A270995", "A279785", "A279788", "A296119", "A304969", "A317532", "A317583", "A318360", "A321469", "A326517", "A326518", "A326520", "A326535", "A331638", "A333217", "A381633", "A381635", "A381636", "A381716", "A381718", "A381806", "A381870", "A381996", "A382080", "A382203", "A382204", "A382214", "A382216", "A382429" ]
null
Gus Wiseman, Mar 26 2025
2025-04-06T14:05:06
oeisdata/seq/A382/A382429.seq
0a7555c20eb6752ddb4a5a253f26c88a
A382430
Number of non-isomorphic finite multisets of size n that cannot be partitioned into sets with distinct sums.
[ "0", "0", "1", "1", "2", "3", "5", "6", "9", "12", "17", "22", "32" ]
[ "nonn", "more" ]
5
0
5
[ "A050326", "A116539", "A279785", "A292432", "A292444", "A293243", "A358914", "A381633", "A381718", "A381806", "A381990", "A381992", "A381996", "A382075", "A382077", "A382078", "A382200", "A382202", "A382214", "A382216", "A382430", "A382523" ]
null
Gus Wiseman, Apr 01 2025
2025-04-01T10:27:12
oeisdata/seq/A382/A382430.seq
c2ab478d0e627ef4c0990c95947bba99
A382431
Number of minimum dominating sets in the n-Goldberg graph.
[ "63", "12", "5", "1395", "504", "204", "27", "5", "7370", "1728", "390", "42", "5", "21052", "3825", "621", "57", "5", "46011", "6930", "897", "72", "5", "86216", "11178", "1218", "87", "5", "146041", "16704", "1584", "102", "5", "230265", "23643", "1995", "117", "5", "344072", "32130", "2451", "132", "5", "493051", "42300", "2952", "147", "5", "683196", "54288", "3498", "162", "5" ]
[ "nonn", "easy" ]
24
3
1
[ "A364668", "A382384", "A382431", "A382657" ]
null
Eric W. Weisstein, Mar 25 2025
2025-05-31T09:34:41
oeisdata/seq/A382/A382431.seq
a285f143b422d4b38dc64f528cc1f367
A382432
a(n) = A074829(2*n-1, n).
[ "1", "2", "8", "30", "114", "436", "1676", "6468", "25040", "97190", "378050", "1473254", "5750390", "22476090", "87958306", "344593314", "1351330642", "5303953012", "20834616860", "81900891372", "322168053848", "1268071841744", "4994044075204", "19678407053280", "77578340524444", "305977596195556", "1207325722552016", "4765772559893268" ]
[ "nonn" ]
7
1
2
[ "A074829", "A382432" ]
null
Michel Marcus, Mar 25 2025
2025-03-31T06:48:05
oeisdata/seq/A382/A382432.seq
0347c827d5b5a24700298b77f3a528b1
A382433
a(n) = S(6,n), where S(r,n) = Sum_{k=0..floor(n/2)} ( binomial(n,k) - binomial(n,k-1) )^r.
[ "1", "1", "2", "65", "794", "19722", "562692", "15105729", "553537490", "18107304842", "716747344436", "27247858130506", "1137502720488532", "47573235297987700", "2085487143991309320", "92820152112054862785", "4246321874111740074210", "197525644801830489637170", "9363425291004877645851300" ]
[ "nonn" ]
19
0
3
[ "A000108", "A008315", "A120730", "A129123", "A357824", "A382433", "A382435" ]
null
Seiichi Manyama, Mar 25 2025
2025-04-01T20:09:29
oeisdata/seq/A382/A382433.seq
6f9965406cb5395af8d45fddb0c57dc1
A382434
a(n) = Sum_{k=0..n} ( binomial(n,k) - binomial(n,k-1) )^4.
[ "1", "1", "3", "33", "195", "1763", "15623", "156257", "1630947", "17911299", "203739015", "2389928995", "28749060871", "353362388551", "4424242664975", "56290517376737", "726355164976547", "9490129871680355", "125375330053632455", "1672895457018337859", "22522481793315373319", "305695116823973096519" ]
[ "nonn" ]
19
0
3
[ "A080233", "A129123", "A131428", "A156644", "A382434", "A382435" ]
null
Seiichi Manyama, Mar 25 2025
2025-03-31T06:30:46
oeisdata/seq/A382/A382434.seq
3618db99bd2eafbdf02c7ea31da326e8
A382435
a(n) = Sum_{k=0..n} ( binomial(n,k) - binomial(n,k-1) )^6.
[ "1", "1", "3", "129", "1587", "39443", "1125383", "30211457", "1107074979", "36214609683", "1433494688871", "54495716261011", "2275005440977063", "95146470595975399", "4170974287982618639", "185640304224109725569", "8492643748223480148419", "395051289603660979274339", "18726850582009755291702599" ]
[ "nonn" ]
15
0
3
[ "A080233", "A131428", "A156644", "A382433", "A382434", "A382435" ]
null
Seiichi Manyama, Mar 25 2025
2025-03-25T12:56:36
oeisdata/seq/A382/A382435.seq
3a998646deadd7545a6240294617d120
A382436
Triangle read by rows, defined by the two-variable g.f. 1/(1 - (y + 1)*x - y*x^2 - (y^2 + y)*x^3).
[ "1", "1", "1", "1", "3", "1", "1", "6", "6", "1", "1", "9", "17", "9", "1", "1", "12", "36", "36", "12", "1", "1", "15", "64", "101", "64", "15", "1", "1", "18", "101", "227", "227", "101", "18", "1", "1", "21", "147", "440", "627", "440", "147", "21", "1", "1", "24", "202", "767", "1459", "1459", "767", "202", "24", "1", "1", "27", "266", "1235", "2994", "3999", "2994", "1235", "266", "27", "1" ]
[ "nonn", "tabl", "changed" ]
30
0
5
[ "A008288", "A056594", "A077938", "A103450", "A339565", "A382436", "A382444" ]
null
F. Chapoton, Mar 25 2025
2025-07-09T05:08:47
oeisdata/seq/A382/A382436.seq
2798e26348fff0e2b3735803767e270d
A382437
a(n) = a(n-1)^2 + 4 * a(n-1), with a(0) = 2.
[ "2", "12", "192", "37632", "1416317952", "2005956546822746112", "4023861667741036022825635656102100992", "16191462721115671781777559070120513664958590125499158514329308740975788032" ]
[ "nonn" ]
25
0
1
[ "A002812", "A003010", "A382437" ]
null
V. Barbera, Mar 25 2025
2025-04-06T22:18:05
oeisdata/seq/A382/A382437.seq
b07bac2dbd7bbc1bb10d885d8ba37d3a
A382438
Numbers k in A024619 such that all residues r (mod k) in row k of A381801 are such that rad(r) divides k, where rad = A007947.
[ "6", "12", "14", "24", "39", "62", "155", "254", "3279", "5219", "16382", "19607", "70643", "97655", "208919", "262142", "363023", "402233", "712979", "1040603", "1048574", "1508597", "2265383", "2391483", "4685519", "5207819", "6728903", "21243689", "25239899", "56328959", "61035155", "67977559", "150508643" ]
[ "nonn" ]
36
1
1
[ "A007947", "A024619", "A381750", "A381801", "A382438" ]
null
Michael De Vlieger, Mar 27 2025
2025-05-31T05:52:30
oeisdata/seq/A382/A382438.seq
1729d8c231b6c9a1ba1f9c9785ef2feb
A382439
Triangle read by rows: defined by the two-variable g.f. (x^3*y^2 + x^3*y - x^2*y + 1) / (1 - x^2*y - x*y - x).
[ "1", "1", "1", "1", "2", "1", "1", "5", "5", "1", "1", "7", "12", "7", "1", "1", "9", "24", "24", "9", "1", "1", "11", "40", "60", "40", "11", "1", "1", "13", "60", "124", "124", "60", "13", "1", "1", "15", "84", "224", "308", "224", "84", "15", "1", "1", "17", "112", "368", "656", "656", "368", "112", "17", "1", "1", "19", "144", "564", "1248", "1620", "1248", "564", "144", "19", "1" ]
[ "nonn", "tabl" ]
27
0
5
[ "A008288", "A245990", "A382436", "A382439" ]
null
F. Chapoton, Mar 25 2025
2025-03-27T10:02:54
oeisdata/seq/A382/A382439.seq
faa6c74f319796a7e40d8833f5da6587
A382440
Number of rooted full binary trees with n internal nodes, up to their multiset of subtree sizes.
[ "1", "1", "2", "3", "6", "11", "23", "45", "95", "194", "414", "863", "1850", "3910", "8413", "17887", "38517", "82249", "177133", "378871", "815265", "1745006", "3750385", "8024725", "17219142", "36817113" ]
[ "nonn", "more" ]
13
1
3
[ "A000108", "A001190", "A247139", "A382440" ]
null
Ludovic Schwob, Mar 25 2025
2025-04-04T15:14:32
oeisdata/seq/A382/A382440.seq
8ad975d3d409df63577bc2c4b15a48bb
A382441
Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose decimal expansion appears as a contiguous subword in the concatenation of the previous terms.
[ "1", "2", "5", "7", "8", "9", "10", "16", "20", "32", "40", "50", "51", "53", "64", "83", "93", "100", "117", "118", "126", "160", "186", "200", "207", "224", "250", "288", "311", "320", "352", "372", "391", "400", "448", "480", "500", "625", "640", "713", "800", "960", "979", "1000", "1011", "1039", "1043", "1097", "1099", "1173", "1200", "1250", "1359", "1426" ]
[ "nonn", "base" ]
13
1
2
[ "A048991", "A382441", "A382442", "A382445" ]
null
Rémy Sigrist, Mar 25 2025
2025-03-28T08:03:26
oeisdata/seq/A382/A382441.seq
8571b3bffeacb87dda91d2bf92bf3a3e
A382442
Lexicographically earliest sequence of positive integers such that for any n > 1, a(n) does not divide any of the positive numbers whose binary expansion appears as a contiguous subword in the concatenation of the previous terms.
[ "1", "2", "4", "7", "8", "16", "18", "27", "32", "42", "54", "64", "84", "126", "128", "133", "172", "238", "256", "276", "379", "381", "444", "512", "524", "582", "621", "765", "948", "1024", "1048", "1179", "1241", "1449", "1496", "1557", "1861", "1896", "1982", "2048", "2132", "2155", "2227", "2386", "2667", "2900", "3013", "3058", "3236", "3444", "3613" ]
[ "nonn", "base" ]
6
1
2
[ "A382441", "A382442" ]
null
Rémy Sigrist, Mar 26 2025
2025-03-28T08:03:30
oeisdata/seq/A382/A382442.seq
5326f59b7d29719a5a80b00e7d3d645f
A382443
a(n) = Sum_{k=0..n} binomial(n,k) * ( binomial(n,k) - binomial(n,k-1) )^4.
[ "1", "1", "4", "65", "566", "10912", "164032", "3237313", "62253130", "1314421886", "28392213224", "639799858304", "14785604868256", "350615631856960", "8485316740880384", "209179475361783233", "5239271305444731698", "133100429387161703962", "3424142506153260211720", "89090362800169426107070" ]
[ "nonn" ]
30
0
3
[ "A000108", "A129123", "A381676", "A382433", "A382434", "A382443", "A382446" ]
null
Seiichi Manyama, Mar 26 2025
2025-03-29T16:25:59
oeisdata/seq/A382/A382443.seq
d033c389d572527ce9cf51c33db4c796
A382444
Triangle read by rows, defined by the two-variable g.f. (1 + y*x^2 + (y^2 + y)*x^3)/(1-(1+y)*x-y*x^2).
[ "1", "1", "1", "1", "4", "1", "1", "7", "7", "1", "1", "9", "18", "9", "1", "1", "11", "34", "34", "11", "1", "1", "13", "54", "86", "54", "13", "1", "1", "15", "78", "174", "174", "78", "15", "1", "1", "17", "106", "306", "434", "306", "106", "17", "1", "1", "19", "138", "490", "914", "914", "490", "138", "19", "1", "1", "21", "174", "734", "1710", "2262", "1710", "734", "174", "21", "1" ]
[ "nonn", "tabl" ]
28
0
5
[ "A008288", "A103450", "A265107", "A382436", "A382444" ]
null
F. Chapoton, Mar 25 2025
2025-03-26T09:18:10
oeisdata/seq/A382/A382444.seq
c73b290b106d15100a6d63fe331b8f25
A382445
Lexicographically least increasing sequence of distinct positive integers such that for any n > 1, a(n) does not divide the concatenation of the earlier terms.
[ "1", "2", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70" ]
[ "nonn", "base" ]
8
1
2
[ "A007978", "A096098", "A382441", "A382445" ]
null
Rémy Sigrist, Mar 25 2025
2025-03-28T08:03:17
oeisdata/seq/A382/A382445.seq
79488196e9cb4283c0fa094bc55f44c0
A382446
a(n) = Sum_{k=0..n} binomial(n,k) * ( binomial(n,k) - binomial(n,k-1) )^6.
[ "1", "1", "4", "257", "4286", "258952", "11816512", "632854273", "43732565914", "2637804065366", "207379028199080", "14568483339859880", "1205457271871693920", "95108827011788280160", "8187664948710535579904", "698818327346476962092801", "62477582066507173352034866", "5627626080883126186936773514" ]
[ "nonn" ]
19
0
3
[ "A000108", "A129123", "A381676", "A382433", "A382435", "A382443", "A382446" ]
null
Seiichi Manyama, Mar 26 2025
2025-03-30T09:52:53
oeisdata/seq/A382/A382446.seq
625c4e1f051b81e303f14e84fbb7f448
A382447
Number of positive k <= n such that k*2^n - 1 is prime.
[ "0", "2", "2", "2", "2", "3", "2", "1", "1", "3", "3", "2", "3", "2", "2", "4", "6", "3", "1", "3", "3", "0", "1", "0", "1", "1", "2", "3", "2", "3", "4", "2", "2", "1", "5", "2", "4", "2", "1", "3", "4", "3", "4", "2", "2", "3", "2", "3", "2", "3", "3", "3", "4", "5", "2", "2", "3", "1", "3", "3", "3", "4", "3", "1", "0", "1", "2", "1", "4", "3", "3", "5", "3", "3", "6", "2", "3", "3", "3", "2", "3", "1", "1", "1", "3", "1", "2", "2", "2", "2", "3", "3", "2", "3", "2", "3", "2", "3", "3", "2" ]
[ "nonn" ]
10
1
2
[ "A002234", "A003261", "A061411", "A061414", "A382119", "A382447" ]
null
Juri-Stepan Gerasimov, Mar 26 2025
2025-04-01T21:30:49
oeisdata/seq/A382/A382447.seq
8c7dc6c36424ae196fac7e03ed5eb2b8
A382448
Triangle read by rows, defined by the two-variable g.f. (x^3*y^2 + x^3*y + 1)/(1 - x^2*y - x*y - x).
[ "1", "1", "1", "1", "3", "1", "1", "6", "6", "1", "1", "8", "15", "8", "1", "1", "10", "29", "29", "10", "1", "1", "12", "47", "73", "47", "12", "1", "1", "14", "69", "149", "149", "69", "14", "1", "1", "16", "95", "265", "371", "265", "95", "16", "1", "1", "18", "125", "429", "785", "785", "429", "125", "18", "1", "1", "20", "159", "649", "1479", "1941", "1479", "649", "159", "20", "1" ]
[ "nonn", "tabl" ]
12
0
5
[ "A008288", "A103450", "A105082", "A382436", "A382444", "A382448" ]
null
F. Chapoton, Mar 26 2025
2025-03-27T10:12:29
oeisdata/seq/A382/A382448.seq
7fc7d1feed5a53f69287adf16f508f7a
A382449
Expansion of e.g.f. exp( x/(1-2*x)^(3/2) ).
[ "1", "1", "7", "64", "745", "10576", "177121", "3414622", "74389729", "1805424040", "48264466321", "1408241206186", "44508262018177", "1514115583435924", "55142123112150985", "2139885098048098486", "88128888655032851521", "3838126991973342097072", "176206944426651875454049" ]
[ "nonn", "easy" ]
32
0
3
[ "A001879", "A362204", "A382449" ]
null
Seiichi Manyama, Apr 03 2025
2025-04-13T03:25:29
oeisdata/seq/A382/A382449.seq
2fdd34623ab61095f11d137f9d5e042b
A382450
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(2*x*A(x)) ).
[ "1", "1", "3", "19", "221", "4597", "174007", "12328367", "1674839513", "443624694633", "231531387336683", "239620527240665643", "493608618766634690997", "2028225390820399637729437", "16643586506902581140427736799", "272938023130910288846692573380167", "8947998686305041917555662919172783921" ]
[ "nonn" ]
28
0
3
[ "A382450", "A384777" ]
null
Seiichi Manyama, Jun 10 2025
2025-06-10T13:57:22
oeisdata/seq/A382/A382450.seq
3c758bf6587932e0c089526de17cb27a
A382451
Centered pentagonal numbers which are the products of four distinct primes.
[ "5406", "12426", "20026", "23766", "40641", "55131", "83266", "115026", "118266", "136306", "142206", "145806", "176226", "184281", "205206", "209526", "245706", "279726", "284766", "315951", "326706", "371526", "387106", "407031", "413106", "419226", "425391", "498406", "505126", "553426", "623751", "638826", "672106", "685131" ]
[ "nonn" ]
8
1
1
[ "A005891", "A046386", "A364610", "A382451" ]
null
Massimo Kofler, Mar 26 2025
2025-03-31T21:27:11
oeisdata/seq/A382/A382451.seq
a6b0aae4914fea927e94bc6193604bd4
A382452
Number of self numbers <= 10^n.
[ "5", "13", "102", "983", "9784", "97786", "977787", "9777788", "97777789", "977777790", "9777777791" ]
[ "nonn", "base", "more" ]
14
1
1
[ "A003052", "A382452" ]
null
Shyam Sunder Gupta, Mar 27 2025
2025-04-01T23:14:31
oeisdata/seq/A382/A382452.seq
1dd66e19fd9b66d49904f26092dcc52d
A382453
Lexicographically earliest sequence of distinct terms such that no term is a substring of the sum of any two terms.
[ "1", "3", "21", "23", "25", "39", "41", "43", "45", "47", "49", "221", "223", "241", "243", "2001", "2003", "2021", "2023", "2025", "2039", "2041", "2043", "2045", "2047", "2049", "2221", "2223", "2241", "2243", "2601", "2603", "2621", "2623", "2639", "2641", "2643", "2645", "4001", "4003", "4021", "4023", "4025", "4039", "4041", "4043", "4045", "4047" ]
[ "nonn", "base" ]
8
1
2
[ "A381242", "A382453" ]
null
Dominic McCarty, Mar 26 2025
2025-03-26T21:47:47
oeisdata/seq/A382/A382453.seq
c5b6282be896627ccf4eeb70e2b48361
A382454
Number of solutions winning the Tchoukaillon game with n seeds and 2n pits.
[ "1", "2", "9", "49", "285", "1717", "10569", "66013", "416687", "2651355", "16976806", "109256095", "706071989", "4579020513", "29784426945", "194231327451", "1269457354069", "8313189986612", "54534379879411", "358298017624625", "2357331709694072", "15528887031395023", "102412421113465576", "676104332189192702" ]
[ "nonn" ]
40
0
2
[ "A000707", "A008302", "A382454" ]
null
Darío Clavijo, May 26 2025
2025-06-02T18:28:06
oeisdata/seq/A382/A382454.seq
05b50edc0d3de338c444ea58840329b3
A382455
Order 3 perimeter magic squares of magic sum n, all elements distinct and 1 in the set; bracelet symmetry.
[ "3", "9", "23", "45", "75", "109", "178", "220", "324", "403", "545", "623", "872", "945", "1238", "1397", "1725", "1878", "2390", "2530", "3087", "3317", "3968", "4212", "5057", "5256", "6186", "6569", "7569", "7893", "9201", "9511", "10890", "11359", "12863", "13340", "15135", "15543", "17492", "18145", "20170", "20739", "23212", "23784", "26325", "27100", "29813", "30598", "33727" ]
[ "nonn" ]
6
12
1
[ "A084569", "A380962", "A382455" ]
null
R. J. Mathar, Mar 26 2025
2025-03-26T13:26:16
oeisdata/seq/A382/A382455.seq
ef79a52171cdd3e5b4cf69039895d735
A382456
Number of self-primes <= 10^n.
[ "3", "6", "21", "115", "836", "6943", "63113", "585517", "5263827", "45808290", "398309972" ]
[ "nonn", "base", "more" ]
5
1
1
[ "A003052", "A006378", "A006880", "A382452", "A382456" ]
null
Shyam Sunder Gupta, Mar 27 2025
2025-04-01T23:15:12
oeisdata/seq/A382/A382456.seq
125d720e6c9bcd967defa2140ecd2143
A382457
Number of twin self-primes <= 10^n.
[ "2", "2", "2", "2", "12", "87", "534", "3683", "27738", "231431", "2061879" ]
[ "nonn", "base", "more" ]
11
1
1
[ "A003052", "A006378", "A006880", "A007508", "A380713", "A380715", "A382452", "A382456", "A382457" ]
null
Shyam Sunder Gupta, Mar 27 2025
2025-04-04T04:18:17
oeisdata/seq/A382/A382457.seq
99917ecdfbc47bf729978c14578c354d
A382458
Number of normal multisets of size n that can be partitioned into a set of sets in exactly one way.
[ "1", "1", "0", "2", "1", "3", "0", "7", "3", "11", "18", "9" ]
[ "nonn", "more" ]
8
0
4
[ "A000045", "A000110", "A000670", "A007716", "A034691", "A035310", "A050320", "A050326", "A050342", "A089259", "A116539", "A116540", "A255903", "A255906", "A270995", "A275780", "A279785", "A292432", "A292444", "A293243", "A293511", "A296119", "A296120", "A302478", "A302494", "A317532", "A318360", "A318361", "A326519", "A358914", "A381633", "A381718", "A381806", "A381870", "A381990", "A381992", "A381996", "A382075", "A382077", "A382078", "A382079", "A382200", "A382201", "A382428", "A382430", "A382458", "A382459", "A382460", "A382523" ]
null
Gus Wiseman, Mar 30 2025
2025-03-31T21:55:36
oeisdata/seq/A382/A382458.seq
ff5076f81032893e2118e5c54f1080fe
A382459
Number of normal multisets of size n that can be partitioned into a set of sets with distinct sums in exactly one way.
[ "1", "1", "0", "2", "1", "3", "2", "7", "4", "10", "19" ]
[ "nonn", "more" ]
7
0
4
[ "A000110", "A000670", "A007716", "A034691", "A035310", "A050320", "A050326", "A050342", "A089259", "A116539", "A116540", "A255903", "A255906", "A270995", "A275780", "A279785", "A292432", "A292444", "A293243", "A293511", "A296119", "A296120", "A302478", "A302494", "A317532", "A318360", "A318361", "A321469", "A326519", "A358914", "A381078", "A381441", "A381633", "A381718", "A381806", "A381870", "A381990", "A381992", "A381996", "A382075", "A382077", "A382078", "A382079", "A382200", "A382201", "A382202", "A382214", "A382216", "A382428", "A382430", "A382458", "A382459", "A382460", "A382523" ]
null
Gus Wiseman, Apr 01 2025
2025-04-03T20:34:46
oeisdata/seq/A382/A382459.seq
7d52eecd41ae6645d132743b664e5a23
A382460
Number of integer partitions of n that can be partitioned into sets with distinct sums in exactly one way.
[ "1", "1", "1", "1", "2", "3", "3", "4", "6", "5", "10", "10", "13", "15", "22", "20", "32", "32", "43", "49", "65", "64", "92", "96", "121", "140", "173", "192" ]
[ "nonn", "more" ]
7
0
5
[ "A000009", "A000041", "A002846", "A047966", "A050320", "A050326", "A050342", "A089259", "A116539", "A116540", "A213427", "A265947", "A270995", "A279785", "A293243", "A293511", "A296119", "A296120", "A299202", "A302478", "A317142", "A318360", "A318361", "A358914", "A381441", "A381454", "A381633", "A381636", "A381718", "A381806", "A381870", "A381990", "A381991", "A381992", "A382075", "A382077", "A382078", "A382079", "A382200", "A382201", "A382301", "A382460" ]
null
Gus Wiseman, Mar 29 2025
2025-03-31T21:55:50
oeisdata/seq/A382/A382460.seq
0299474ae9b4cc7a1262b77238e94695
A382461
a(n) is the smallest number whose sum of digits is 2^n.
[ "1", "2", "4", "8", "79", "5999", "19999999", "299999999999999", "49999999999999999999999999999", "899999999999999999999999999999999999999999999999999999999", "799999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" ]
[ "nonn", "base", "easy" ]
10
0
2
[ "A000079", "A007953", "A051885", "A054750", "A060712", "A136308", "A180083", "A382461" ]
null
Stefano Spezia, Mar 27 2025
2025-03-30T09:53:19
oeisdata/seq/A382/A382461.seq
e7cce4e080d23acfaee46d2bad7e23dd
A382462
Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "13", "14", "15", "16", "17", "18", "19", "31", "21", "23", "33", "34", "35", "36", "37", "38", "39", "51", "24", "53", "41", "25", "55", "56", "57", "58", "59", "71", "26", "73", "43", "45", "61", "27", "75", "63", "46", "77", "78", "79", "91", "28", "93", "47", "81", "29", "95", "65", "67", "83", "48", "97", "85", "68", "99", "111", "49", "112", "69" ]
[ "nonn", "base", "look" ]
25
1
2
[ "A342042", "A342043", "A342044", "A342045", "A382462", "A382463", "A382464", "A382465", "A382466", "A382621", "A382935", "A383059" ]
null
Paolo Xausa, Mar 27 2025
2025-05-13T11:34:11
oeisdata/seq/A382/A382462.seq
4f49a3dce7f239815abb75c5f00d9870
A382463
First differences of A382462.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "12", "-10", "2", "10", "1", "1", "1", "1", "1", "1", "12", "-27", "29", "-12", "-16", "30", "1", "1", "1", "1", "12", "-45", "47", "-30", "2", "16", "-34", "48", "-12", "-17", "31", "1", "1", "12", "-63", "65", "-46", "34", "-52", "66", "-30", "2", "16", "-35", "49", "-12", "-17", "31", "12", "-62", "63", "-43", "44" ]
[ "sign", "base" ]
5
1
9
[ "A382462", "A382463" ]
null
Paolo Xausa, Mar 28 2025
2025-03-29T18:12:17
oeisdata/seq/A382/A382463.seq
63af435107e92cc9e5e7600547774f4e
A382464
Positive integers that contain an even digit d immediately preceded by a digit >= d.
[ "10", "20", "22", "30", "32", "40", "42", "44", "50", "52", "54", "60", "62", "64", "66", "70", "72", "74", "76", "80", "82", "84", "86", "88", "90", "92", "94", "96", "98", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "120", "122", "130", "132", "140", "142", "144", "150", "152", "154", "160", "162", "164", "166", "170", "172", "174", "176", "180" ]
[ "nonn", "base", "easy" ]
16
1
1
[ "A347298", "A382462", "A382464", "A382465", "A382623", "A382937", "A383061", "A383245", "A383247", "A383249", "A383500" ]
null
Paolo Xausa, Mar 28 2025
2025-04-30T11:09:02
oeisdata/seq/A382/A382464.seq
6d6a8f36a4377ec7610cb1c12630daf8
A382465
Positive integers such that every even digit except the first is immediately preceded by a smaller digit.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "13", "14", "15", "16", "17", "18", "19", "21", "23", "24", "25", "26", "27", "28", "29", "31", "33", "34", "35", "36", "37", "38", "39", "41", "43", "45", "46", "47", "48", "49", "51", "53", "55", "56", "57", "58", "59", "61", "63", "65", "67", "68", "69", "71", "73", "75", "77", "78", "79", "81", "83", "85", "87", "89", "91", "93", "95", "97", "99" ]
[ "nonn", "base", "easy" ]
14
1
2
[ "A377912", "A382462", "A382464", "A382465", "A382624", "A382938", "A383062", "A383246", "A383248", "A383250", "A383501" ]
null
Paolo Xausa, Mar 28 2025
2025-04-30T11:08:58
oeisdata/seq/A382/A382465.seq
9a015021102a8af236eaf2d3f9a73dd1
A382466
Split A382462 into runs of increasing elements. a(n) is the length of the n-th run.
[ "19", "10", "2", "1", "7", "2", "3", "2", "1", "5", "2", "2", "2", "3", "2", "1", "3", "2", "2", "61", "11", "9", "8", "8", "7", "7", "6", "6", "3", "2", "4", "8", "2", "8", "2", "7", "2", "6", "2", "6", "2", "1", "8", "2", "5", "2", "2", "2", "1", "2", "1", "6", "2", "2", "1", "1", "2", "8", "6", "2", "6", "3", "2", "1", "5", "2", "2", "1", "4", "2", "1", "2", "6", "6", "3", "2", "2", "2", "2", "1", "2", "1", "2", "1", "1", "5", "5", "4", "2", "2", "4" ]
[ "nonn", "base" ]
16
1
1
[ "A382462", "A382466" ]
null
Paolo Xausa, Mar 28 2025
2025-03-31T11:56:12
oeisdata/seq/A382/A382466.seq
7a62bab00fcde6cda7e5abef6f48833a
A382467
Irregular triangle read by rows, where row n lists the integers from 0 to 2^n - 1 sorted by the number of zeros in their binary representation (in case of ties, by their decimal value).
[ "0", "0", "1", "0", "1", "3", "2", "0", "1", "3", "7", "2", "5", "6", "4", "0", "1", "3", "7", "15", "2", "5", "6", "11", "13", "14", "4", "9", "10", "12", "8", "0", "1", "3", "7", "15", "31", "2", "5", "6", "11", "13", "14", "23", "27", "29", "30", "4", "9", "10", "12", "19", "21", "22", "25", "26", "28", "8", "17", "18", "20", "24", "16", "0", "1", "3", "7", "15", "31", "63", "2", "5", "6", "11", "13", "14", "23", "27", "29", "30" ]
[ "nonn", "tabf", "look", "base", "easy" ]
16
0
6
[ "A000225", "A006516", "A080791", "A131577", "A294648", "A382467" ]
null
Paolo Xausa, Mar 31 2025
2025-04-02T18:48:40
oeisdata/seq/A382/A382467.seq
4efad31ef5d13a608c5046ee2a0ca692
A382468
a(n) = (largest prime factor of n) minus (its remaining distinct prime factors).
[ "2", "3", "2", "5", "1", "7", "2", "3", "3", "11", "1", "13", "5", "2", "2", "17", "1", "19", "3", "4", "9", "23", "1", "5", "11", "3", "5", "29", "0", "31", "2", "8", "15", "2", "1", "37", "17", "10", "3", "41", "2", "43", "9", "2", "21", "47", "1", "7", "3", "14", "11", "53", "1", "6", "5", "16", "27", "59", "0", "61", "29", "4", "2", "8", "6", "67", "15", "20", "0", "71", "1", "73", "35", "2", "17", "4", "8", "79", "3", "3" ]
[ "sign", "easy" ]
20
2
1
[ "A006530", "A008472", "A027748", "A212665", "A215142", "A382468", "A382469" ]
null
Paolo Xausa, Mar 31 2025
2025-04-01T05:43:50
oeisdata/seq/A382/A382468.seq
cf6e711d70b789391ace80d4abf07761
A382469
Numbers k such that the largest prime factor of k equals the sum of its remaining distinct prime factors.
[ "30", "60", "70", "90", "120", "140", "150", "180", "240", "270", "280", "286", "300", "350", "360", "450", "480", "490", "540", "560", "572", "600", "646", "700", "720", "750", "810", "900", "960", "980", "1080", "1120", "1144", "1200", "1292", "1350", "1400", "1440", "1500", "1620", "1750", "1798", "1800", "1920", "1960", "2160", "2240", "2250", "2288", "2400", "2430", "2450", "2584", "2700", "2800", "2880", "3000", "3135", "3146", "3240" ]
[ "nonn" ]
19
1
1
[ "A006530", "A027748", "A071140", "A221054", "A365795", "A382468", "A382469" ]
null
Paolo Xausa, Mar 31 2025
2025-05-31T19:26:42
oeisdata/seq/A382/A382469.seq
99921200f720b1a9cb5358d4b722211b
A382470
a(n) = Sum_{k=0..n} binomial(k+3,3) * binomial(2*k,2*n-2*k).
[ "1", "4", "14", "80", "345", "1336", "5074", "18404", "64460", "220276", "736242", "2415128", "7798043", "24833160", "78131242", "243211412", "749926963", "2292771088", "6956262660", "20959406680", "62753991192", "186809711448", "553172044548", "1630068765840", "4781871397429", "13969460520764" ]
[ "nonn", "easy" ]
21
0
2
[ "A034839", "A108479", "A377148", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-10T12:58:11
oeisdata/seq/A382/A382470.seq
bfc95b0eb03f3f9ce1e5a00f78b80364
A382471
a(n) = Sum_{k=0..n} binomial(k+4,4) * binomial(2*k,2*n-2*k).
[ "1", "5", "20", "125", "610", "2611", "10815", "42610", "161005", "590155", "2106362", "7348265", "25141430", "84569395", "280246795", "916465742", "2961805180", "9470735650", "29994694130", "94172180660", "293326457342", "907028460410", "2786036875580", "8505001839950", "25815678641935", "77945771624609" ]
[ "nonn", "easy" ]
20
0
2
[ "A034839", "A108479", "A377152", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-10T14:57:13
oeisdata/seq/A382/A382471.seq
66f84b619d66a15c9dfd4b4e41786317
A382472
a(n) = Sum_{k=0..n} binomial(k+5,5) * binomial(2*k,2*n-2*k).
[ "1", "6", "27", "182", "987", "4620", "20678", "87732", "355095", "1387462", "5258967", "19416222", "70086803", "248046540", "862694058", "2954279732", "9977518122", "33278815920", "109749059308", "358231786128", "1158357919194", "3713416860580", "11810098024410", "37285901203740", "116917784689237" ]
[ "nonn", "easy" ]
19
0
2
[ "A034839", "A108479", "A377153", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-11T01:26:18
oeisdata/seq/A382/A382472.seq
08bb4224852a5a69e286cd49252be6b7
A382473
a(n) = Sum_{k=0..n} binomial(k+6,6) * binomial(2*k,2*n-2*k).
[ "1", "7", "35", "252", "1498", "7602", "36498", "165600", "713769", "2957647", "11850223", "46111352", "174956250", "649284286", "2362771938", "8449241836", "29744151416", "103237104740", "353744829032", "1198001464940", "4013905507150", "13316690882670", "43780154987030", "142726581203640" ]
[ "nonn", "easy" ]
22
0
2
[ "A034839", "A108479", "A377158", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-11T07:59:04
oeisdata/seq/A382/A382473.seq
d661bfc95b22f2c14ca07a0d59af46be
A382474
a(n) = Sum_{k=0..n} binomial(k+7,7) * binomial(2*k,2*n-2*k).
[ "1", "8", "44", "336", "2166", "11832", "60576", "292248", "1334817", "5840296", "24637976", "100684376", "400255050", "1553016960", "5897388492", "21967711160", "80425346844", "289868771928", "1029979010972", "3612517052608", "12520285820362", "42919328903928", "145643017892472", "489606988741128" ]
[ "nonn", "easy" ]
18
0
2
[ "A034839", "A108479", "A377159", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-22T21:54:55
oeisdata/seq/A382/A382474.seq
7bd082fef6445bea7a1c8a806fdae584
A382475
Numbers k where record values occur for A129132(k)/k = A380264(k)/A380265(k), the mean value of the maximum exponent in the prime factorization of the numbers {1, 2, ..., k}.
[ "1", "2", "3", "4", "8", "9", "16", "18", "20", "24", "25", "27", "28", "32", "56", "64", "81", "128", "162", "176", "192", "256", "352", "384", "736", "768", "896", "1026", "1029", "1056", "1280", "1792", "1863", "1864", "1928", "2052", "2058", "2064", "2080", "2304", "2432", "2560", "2944", "3776", "4376", "4384", "4480", "4482", "5104", "5120", "5121", "5125" ]
[ "nonn", "easy", "fini", "full" ]
10
1
2
[ "A033150", "A051903", "A129132", "A380264", "A380265", "A382475", "A382476" ]
null
Amiram Eldar, Mar 28 2025
2025-03-28T08:00:15
oeisdata/seq/A382/A382475.seq
980bc4d2ed910301ad15bf1f5f8e261e
A382476
Numbers k where record low values occur for abs(A129132(k)/k - c) = abs(A380264(k)/A380265(k) - c), where c = A033150 is Niven's constant.
[ "1", "2", "3", "4", "8", "9", "16", "18", "20", "24", "25", "27", "28", "32", "56", "64", "81", "128", "162", "176", "192", "256", "352", "384", "736", "768", "896", "1026", "1029", "1056", "1280", "1792", "1863", "1864", "1928", "2052", "2058", "2064", "2080", "2304", "2432", "2560", "2944", "3776", "4376", "4384", "4480", "4482", "5104", "5120", "5121", "5125" ]
[ "nonn" ]
8
1
2
[ "A033150", "A051903", "A129132", "A380264", "A380265", "A382475", "A382476" ]
null
Amiram Eldar, Mar 28 2025
2025-03-28T08:00:07
oeisdata/seq/A382/A382476.seq
f800125c6ed4e64780a69320e4dd1cda
A382477
If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * k_j * p_j).
[ "0", "2", "3", "-4", "5", "5", "7", "6", "-6", "7", "11", "-1", "13", "9", "8", "-8", "17", "-4", "19", "1", "10", "13", "23", "9", "-10", "15", "9", "3", "29", "10", "31", "10", "14", "19", "12", "-10", "37", "21", "16", "11", "41", "12", "43", "7", "-1", "25", "47", "-5", "-14", "-8", "20", "9", "53", "11", "16", "13", "22", "31", "59", "4", "61", "33", "1", "-12", "18", "16", "67", "13", "26", "14", "71", "0", "73", "39", "-7" ]
[ "sign" ]
39
1
2
[ "A001414", "A008472", "A316523", "A332422", "A332423", "A332424", "A340901", "A366749", "A382331", "A382477" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-17T14:54:39
oeisdata/seq/A382/A382477.seq
dcf38ee633095fb52a8cf7436a2ac03c
A382478
Number of palindromic binary strings of length n having no 4-runs of 1's.
[ "1", "2", "2", "4", "3", "7", "6", "14", "12", "27", "23", "52", "44", "100", "85", "193", "164", "372", "316", "717", "609", "1382", "1174", "2664", "2263", "5135", "4362", "9898", "8408", "19079", "16207", "36776", "31240", "70888", "60217", "136641", "116072", "263384", "223736", "507689", "431265", "978602", "831290", "1886316", "1602363", "3635991", "3088654", "7008598", "5953572" ]
[ "nonn", "easy" ]
18
0
2
[ "A001590", "A001630", "A001631", "A123231", "A251653", "A382478", "A382479" ]
null
R. J. Mathar, Mar 28 2025
2025-05-19T14:57:17
oeisdata/seq/A382/A382478.seq
b21ddab440e02e242fbc8b59b97fdb91
A382479
Number of palindromic binary strings of length n having no 6-runs of 1's.
[ "1", "2", "2", "4", "4", "8", "7", "15", "14", "30", "28", "60", "56", "119", "111", "236", "220", "468", "436", "928", "865", "1841", "1716", "3652", "3404", "7244", "6752", "14369", "13393", "28502", "26566", "56536", "52696", "112144", "104527", "222447", "207338", "441242", "411272", "875240", "815792", "1736111", "1618191", "3443720", "3209816", "6830904", "6366936" ]
[ "nonn", "easy" ]
14
0
2
[ "A001590", "A123231", "A251653", "A251707", "A251708", "A382478", "A382479" ]
null
R. J. Mathar, Mar 28 2025
2025-05-20T15:48:19
oeisdata/seq/A382/A382479.seq
dec47bd8daffd728e93eda01df80c1d4
A382480
Number of minimum connected dominating sets in the n-transposition graph.
[ "1", "2", "9", "18", "28800" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Mar 28 2025
2025-03-28T14:13:14
oeisdata/seq/A382/A382480.seq
adc0a5dcf1d7e2b9b2c7536f567398c6
A382481
a(n) is the number of primes less than 4^(n^2).
[ "0", "2", "54", "23000", "203280221", "33483379603407", "96601075195075186855" ]
[ "nonn", "hard", "more" ]
17
0
2
[ "A000290", "A000302", "A000720", "A007053", "A060757", "A382481" ]
null
Stefano Spezia, Mar 28 2025
2025-03-30T09:53:30
oeisdata/seq/A382/A382481.seq
b2e2bde952bad872def33152d2e100c9
A382482
a(1) = 1. Let a(n) be the most recently defined term. At each step, check for an undefined term with index < n. If such a term exists, then where i is the earliest such index, set a(i) = a(n) - (n - i). If no such term exists, then where i is the first undefined index >= n + a(n), set a(i) = the smallest integer not yet used.
[ "1", "2", "2", "3", "4", "2", "5", "6", "5", "5", "4", "7", "6", "5", "8", "9", "8", "5", "10", "11", "11", "4", "13", "13", "12", "15", "6", "12", "7", "13", "8", "14", "17", "16", "7", "19", "16", "19", "21", "18", "8", "23", "20", "20", "7", "21", "8", "22", "25", "22", "11", "27", "22", "11", "29", "24", "24", "12", "23", "14", "24", "31", "16", "26", "33", "26", "28", "16", "26", "30", "35" ]
[ "look", "nonn" ]
17
1
2
null
null
Sameer Khan, Mar 28 2025
2025-04-03T20:49:27
oeisdata/seq/A382/A382482.seq
54fa6bfb82129729ab3b6d6c9db1282e
A382483
a(n) = smallest number k such that at least one of sigma(n) - k and sigma(n) + k is a perfect number.
[ "5", "3", "2", "1", "0", "6", "2", "9", "7", "10", "6", "0", "8", "4", "4", "3", "10", "11", "8", "14", "4", "8", "4", "32", "3", "14", "12", "28", "2", "44", "4", "35", "20", "26", "20", "63", "10", "32", "28", "62", "14", "68", "16", "56", "50", "44", "20", "96", "29", "65", "44", "70", "26", "92", "44", "92", "52", "62", "32", "140", "34", "68", "76", "99", "56", "116", "40", "98", "68", "116", "44", "167", "46", "86", "96", "112", "68", "140" ]
[ "nonn", "easy" ]
27
1
1
[ "A000396", "A081357", "A146542", "A382483", "A382506" ]
null
Leo Hennig, Mar 27 2025
2025-04-08T21:58:29
oeisdata/seq/A382/A382483.seq
cf38e8bf9bcedf466386a8c9aeba41dc
A382484
Least composite squarefree numbers k > n such that p + n divides k - n, for each prime p dividing k.
[ "385", "182", "195", "1054", "165", "26781", "1015", "4958", "2193", "79222", "5159", "113937", "5593", "160937", "6351", "196009", "3657", "6318638", "2755", "1227818", "12669", "41302", "2795", "152358", "12121", "366821", "21827", "17578", "36569", "12677695", "38335", "457907", "2553", "15334", "141155", "69722351", "1045", "14003", "4823", "2943805" ]
[ "nonn" ]
18
1
1
[ "A208728", "A225702", "A225710", "A225711", "A225720", "A382484" ]
null
Paolo P. Lava, Mar 29 2025
2025-03-30T09:49:12
oeisdata/seq/A382/A382484.seq
fe7cbbadef05eb480641b4ee20f14544
A382485
a(n) = ceiling(n/d^2) where d is the largest divisor of n which is not greater than the square root of n.
[ "1", "2", "3", "1", "5", "2", "7", "2", "1", "3", "11", "2", "13", "4", "2", "1", "17", "2", "19", "2", "3", "6", "23", "2", "1", "7", "3", "2", "29", "2", "31", "2", "4", "9", "2", "1", "37", "10", "5", "2", "41", "2", "43", "3", "2", "12", "47", "2", "1", "2", "6", "4", "53", "2", "3", "2", "7", "15", "59", "2", "61", "16", "2", "1", "3", "2", "67", "5", "8", "2", "71", "2", "73", "19", "3", "5", "2", "3", "79", "2", "1", "21", "83", "2", "4", "22", "10", "2", "89" ]
[ "nonn", "look" ]
64
1
2
[ "A033676", "A033677", "A056737", "A382485" ]
null
Clive Tooth, Mar 30 2025
2025-05-01T01:40:27
oeisdata/seq/A382/A382485.seq
4f9f3ec350ba4ea7436ea9e852a54224
A382486
Product of distinct prime divisors of n that are <= sqrt(n).
[ "1", "1", "1", "2", "1", "2", "1", "2", "3", "2", "1", "6", "1", "2", "3", "2", "1", "6", "1", "2", "3", "2", "1", "6", "5", "2", "3", "2", "1", "30", "1", "2", "3", "2", "5", "6", "1", "2", "3", "10", "1", "6", "1", "2", "15", "2", "1", "6", "7", "10", "3", "2", "1", "6", "5", "14", "3", "2", "1", "30", "1", "2", "21", "2", "5", "6", "1", "2", "3", "70", "1", "6", "1", "2", "15", "2", "7", "6", "1", "10", "3", "2", "1", "42", "5" ]
[ "nonn" ]
24
1
4
[ "A007947", "A007955", "A072499", "A097974", "A382486" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-17T14:54:55
oeisdata/seq/A382/A382486.seq
6c0391dab609de2a4995133a51c4e6ef
A382487
The number of divisors of n whose largest prime factor is 3.
[ "0", "0", "1", "0", "0", "2", "0", "0", "2", "0", "0", "3", "0", "0", "1", "0", "0", "4", "0", "0", "1", "0", "0", "4", "0", "0", "3", "0", "0", "2", "0", "0", "1", "0", "0", "6", "0", "0", "1", "0", "0", "2", "0", "0", "2", "0", "0", "5", "0", "0", "1", "0", "0", "6", "0", "0", "1", "0", "0", "3", "0", "0", "2", "0", "0", "2", "0", "0", "1", "0", "0", "8", "0", "0", "1", "0", "0", "2", "0", "0", "4", "0", "0", "3", "0", "0", "1" ]
[ "nonn", "easy" ]
8
1
6
[ "A001511", "A001651", "A007949", "A051064", "A065119", "A072078", "A169611", "A301461", "A306771", "A382487" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:24:22
oeisdata/seq/A382/A382487.seq
0ae025e31f61d935ccebc2d830da87c1
A382488
The number of unitary 3-smooth divisors of n.
[ "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2" ]
[ "nonn", "easy", "mult" ]
7
1
2
[ "A003586", "A005117", "A034444", "A065331", "A072078", "A134451", "A181982", "A382487", "A382488", "A382489" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:24:09
oeisdata/seq/A382/A382488.seq
84eae8037bd98d81e18e2c531ff29d46
A382489
The number of unitary 5-smooth divisors of n.
[ "1", "2", "2", "2", "2", "4", "1", "2", "2", "4", "1", "4", "1", "2", "4", "2", "1", "4", "1", "4", "2", "2", "1", "4", "2", "2", "2", "2", "1", "8", "1", "2", "2", "2", "2", "4", "1", "2", "2", "4", "1", "4", "1", "2", "4", "2", "1", "4", "1", "4", "2", "2", "1", "4", "2", "2", "2", "2", "1", "8", "1", "2", "2", "2", "2", "4", "1", "2", "2", "4", "1", "4", "1", "2", "4", "2", "1", "4", "1", "4", "2", "2", "1", "4", "2", "2", "2" ]
[ "nonn", "easy", "mult" ]
7
1
2
[ "A002110", "A005117", "A034444", "A051037", "A054640", "A134451", "A236435", "A236436", "A355582", "A355583", "A382488", "A382489" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:23:46
oeisdata/seq/A382/A382489.seq
a8ba53afa360ba26e30faf5bee2ab0e2
A382490
The number of infinitary 3-smooth divisors of n.
[ "1", "2", "2", "2", "1", "4", "1", "4", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "8", "1", "2", "4", "2", "1", "4", "1", "4", "2", "2", "1", "4", "1", "2", "2", "4", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "8", "1", "4", "2", "2", "1", "4", "1", "2", "2", "4", "1", "4", "1", "2", "2", "2", "1", "8", "1", "2", "2", "2", "1", "4", "1", "2", "2", "2", "1", "4", "1", "2", "2" ]
[ "nonn", "easy", "mult" ]
8
1
2
[ "A000120", "A003586", "A007310", "A007814", "A007949", "A036537", "A037445", "A065331", "A138302", "A382488", "A382490" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:23:28
oeisdata/seq/A382/A382490.seq
57adb62d59d6e9cfce241b52e18efd82
A382491
a(n) is the numerator of the asymptotic density of the numbers whose number of 3-smooth divisors is n.
[ "1", "5", "13", "71", "97", "1355", "793", "19163", "53473", "292355", "60073", "13102907", "535537", "78584915", "790859641", "3523099499", "43112257", "99646519235", "387682633", "2764285630427", "7604811750289", "7337148996275", "31385253913", "2226944658077771", "3656440886376673", "2341258386360995", "80539587570991081" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A007310", "A072078", "A081341", "A169604", "A171126", "A382491" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:23:13
oeisdata/seq/A382/A382491.seq
a3f3438bfa42b8eaabc3128e8b27df0b
A382492
a(n) is the least number that has exactly n 3-smooth divisors.
[ "1", "2", "4", "6", "16", "12", "64", "24", "36", "48", "1024", "72", "4096", "192", "144", "216", "65536", "288", "262144", "432", "576", "3072", "4194304", "864", "1296", "12288", "2304", "1728", "268435456", "2592", "1073741824", "3456", "9216", "196608", "5184", "6912", "68719476736", "786432", "36864", "10368", "1099511627776", "15552", "4398046511104" ]
[ "nonn", "easy" ]
12
1
2
[ "A003586", "A005179", "A025487", "A037143", "A046022", "A072078", "A382492", "A382493" ]
null
Amiram Eldar, Mar 29 2025
2025-04-26T03:33:09
oeisdata/seq/A382/A382492.seq
b0f8ab7bbb77ebcb68542f8f1e45ebea
A382493
a(n) is the 2-adic valuation of the least number that has exactly n 3-smooth divisors.
[ "0", "1", "2", "1", "4", "2", "6", "3", "2", "4", "10", "3", "12", "6", "4", "3", "16", "5", "18", "4", "6", "10", "22", "5", "4", "12", "8", "6", "28", "5", "30", "7", "10", "16", "6", "8", "36", "18", "12", "7", "40", "6", "42", "10", "8", "22", "46", "7", "6", "9", "16", "12", "52", "8", "10", "7", "18", "28", "58", "9", "60", "30", "8", "7", "12", "10", "66", "16", "22", "9", "70", "11", "72", "36", "14" ]
[ "nonn", "easy" ]
9
1
3
[ "A007814", "A007949", "A037143", "A099311", "A382492", "A382493" ]
null
Amiram Eldar, Mar 29 2025
2025-03-29T04:22:53
oeisdata/seq/A382/A382493.seq
0d3840137eafcd743ac4fad7fa532c92
A382494
a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,2) * binomial(2*k,2*n-4*k).
[ "1", "0", "3", "3", "6", "36", "16", "150", "165", "430", "1071", "1365", "4453", "6258", "14841", "29169", "49941", "115356", "190091", "404811", "750792", "1393956", "2808438", "4988268", "9905746", "18207126", "34231566", "65278964", "119255889", "227648406", "418394087", "782045001", "1457704212", "2681909302" ]
[ "nonn", "easy" ]
19
0
3
[ "A034839", "A376729", "A377146", "A382230", "A382300", "A382494", "A382495" ]
null
Seiichi Manyama, Mar 29 2025
2025-05-11T22:05:08
oeisdata/seq/A382/A382494.seq
7a667548a06e9d438e97680a3522ef2c
A382495
a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,3) * binomial(2*k,2*n-4*k).
[ "1", "0", "4", "4", "10", "60", "30", "300", "335", "1000", "2506", "3500", "11879", "17304", "44220", "88592", "161865", "385704", "660964", "1475100", "2807956", "5459860", "11313094", "20816004", "42774780", "80798128", "157292750", "307887904", "579776799", "1138007940", "2146348214", "4126143900", "7878910238", "14878269368" ]
[ "nonn", "easy" ]
16
0
3
[ "A034839", "A376729", "A382300", "A382470", "A382494", "A382495" ]
null
Seiichi Manyama, Mar 29 2025
2025-05-12T10:13:57
oeisdata/seq/A382/A382495.seq
85fa115c915c80f4b6bada5efca06e28
A382496
a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(2*k,2*n-6*k).
[ "1", "0", "0", "2", "2", "0", "3", "18", "3", "4", "60", "60", "9", "140", "350", "146", "275", "1260", "1267", "732", "3471", "6476", "4193", "8470", "24040", "25104", "24388", "72810", "117368", "102672", "202031", "440750", "490884", "612012", "1419042", "2121626", "2281049", "4267188", "7951185", "9511604", "13402924", "26600984", "38465043", "47376620" ]
[ "nonn", "easy" ]
19
0
4
[ "A034839", "A375470", "A381421", "A382300", "A382496" ]
null
Seiichi Manyama, Mar 29 2025
2025-05-12T10:13:53
oeisdata/seq/A382/A382496.seq
d9aa21cc95f50084f79eb836a9c1edb4
A382497
Decimal expansion of 3*log(x0)/(log(8*x0/3) - 8 + Pi/sqrt(3)), where x0 is the unique real root of 96*x^3 - 786663*x^2 + 17288*x - 96 = 0.
[ "7", "1", "0", "3", "2", "0", "5", "3", "3", "4", "1", "3", "7", "0", "0", "1", "7", "2", "7", "5", "0", "5", "7", "7", "3", "4", "2", "2", "8", "1", "0", "3", "0", "8", "4", "9", "8", "5", "2", "4", "7", "8", "9", "9", "9", "1", "7", "8", "7", "1", "8", "0", "8", "3", "3", "7", "8", "1", "3", "9", "9", "7", "1", "7", "9", "7", "3", "1", "3", "5", "8", "9", "5", "2", "1", "4", "6", "4", "6", "1", "0", "5", "9", "9", "6", "4", "2", "2", "1", "1" ]
[ "nonn", "cons" ]
16
1
1
[ "A000796", "A002194", "A093602", "A382497" ]
null
Jianing Song, Mar 29 2025
2025-05-12T00:28:50
oeisdata/seq/A382/A382497.seq
182733ac4f21517107e39b852c8ebe8f
A382498
Smallest k such that the fractional part of 1/k is pandigital in base n.
[ "3", "5", "13", "7", "11", "11", "11", "43", "17", "13", "17", "19", "17", "19", "79", "23", "29", "23", "23", "23", "31", "47", "31", "73", "29", "29", "41", "41", "41", "47", "37", "43", "41", "37", "137", "59", "47", "47", "47", "47", "59", "47", "47", "47", "67", "59", "53", "241", "53", "53", "59", "71", "59", "59", "59", "67", "73", "61", "73", "67", "71", "67", "383", "71", "79" ]
[ "nonn", "base" ]
18
2
1
[ "A001913", "A261773", "A382498" ]
null
Joshua Searle, Mar 29 2025
2025-03-30T12:49:10
oeisdata/seq/A382/A382498.seq
d64e3e53941551a0c73d7d52fee6c5bc
A382499
Inverse permutation to A381968.
[ "1", "5", "3", "4", "2", "6", "12", "8", "14", "10", "11", "9", "13", "7", "15", "23", "17", "25", "19", "27", "21", "22", "20", "24", "18", "26", "16", "28", "38", "30", "40", "32", "42", "34", "44", "36", "37", "35", "39", "33", "41", "31", "43", "29", "45", "57", "47", "59", "49", "61", "51", "63", "53", "65", "55", "56", "54", "58", "52", "60", "50", "62", "48", "64", "46", "66" ]
[ "nonn", "tabf" ]
18
1
2
[ "A000027", "A000384", "A016813", "A056023", "A376214", "A378684", "A378762", "A379342", "A379343", "A380200", "A380245", "A380815", "A380817", "A381662", "A381663", "A381664", "A381968", "A382499", "A382679", "A382680", "A383419", "A383589", "A383590", "A383722", "A383723", "A383724" ]
null
Boris Putievskiy, Mar 29 2025
2025-05-30T23:30:53
oeisdata/seq/A382/A382499.seq
efa6512bc0e3a7110b3e3358cec46565
A382500
Number of minimum connected dominating sets in the n-flower graph.
[ "1", "9", "6", "219", "20", "1968", "56", "10779", "144", "52488", "352", "231984", "832", "977133", "1920", "3966699", "4352", "15720639", "9728", "61191312", "21504", "235009107", "47104", "893270016", "102400", "3367409412", "221184", "12609435873", "475136", "46953650535", "1015808", "174014499435", "2162688", "642287275092", "4587520", "2362247579547" ]
[ "nonn", "easy" ]
9
1
2
[ "A362807", "A382500" ]
null
Eric W. Weisstein, Mar 29 2025
2025-05-24T19:01:03
oeisdata/seq/A382/A382500.seq
eb5d53466b3c8a9bdfa03cf21362480a
A382501
Lexicographically earliest infinite sequence of positive integers such that, for any given k, every subsequence {a(j), a(j+k), a(j+2k)} (j, k >= 1) is unique.
[ "1", "1", "1", "2", "1", "1", "3", "1", "2", "4", "3", "1", "1", "4", "1", "3", "2", "5", "2", "4", "2", "3", "4", "1", "2", "5", "3", "2", "4", "6", "1", "3", "5", "5", "6", "1", "1", "7", "2", "3", "8", "4", "8", "7", "1", "2", "6", "5", "3", "1", "4", "3", "8", "7", "2", "8", "2", "6", "9", "1", "9", "1", "4", "6", "9", "4", "5", "9", "2", "7", "5", "7", "3", "4", "3", "10", "10", "4", "9", "1", "3", "6", "2", "5", "8", "2", "9" ]
[ "nonn" ]
12
1
4
[ "A364057", "A382501", "A382502" ]
null
Neal Gersh Tolunsky, Mar 29 2025
2025-04-06T16:49:26
oeisdata/seq/A382/A382501.seq
84bea887338b9f302ea212859c279098
A382502
Lexicographically earliest sequence of positive integers such that no two subsequences {a(j), a(j+k), a(j+2k)} and {a(i), a(i+m), a(i+2m)} with different k and m values are the same.
[ "1", "1", "1", "2", "3", "1", "2", "3", "4", "5", "6", "7", "8", "1", "9", "2", "3", "4", "5", "6", "1", "10", "7", "8", "11", "9", "12", "7", "10", "5", "13", "12", "14", "4", "6", "15", "16", "11", "17", "8", "18", "2", "3", "9", "5", "18", "1", "19", "14", "5", "15", "4", "20", "21", "13", "12", "22", "23", "24", "2", "21", "11", "25", "8", "26", "16", "20", "3", "27", "17", "12", "28", "29", "30", "31" ]
[ "nonn" ]
19
1
4
[ "A364057", "A382501", "A382502" ]
null
Neal Gersh Tolunsky, Mar 29 2025
2025-04-07T08:09:53
oeisdata/seq/A382/A382502.seq
af69c47626201f347255f59762e8af0f
A382503
a(n) = Sum_{d|n} binomial(2*d-1,d).
[ "1", "4", "11", "39", "127", "476", "1717", "6474", "24321", "92508", "352717", "1352589", "5200301", "20060020", "77558897", "300546669", "1166803111", "4537592436", "17672631901", "68923356953", "269128938947", "1052049834580", "4116715363801", "16123803200574", "63205303219003", "247959271674356" ]
[ "nonn" ]
35
1
2
[ "A000005", "A000984", "A001700", "A045630", "A072929", "A088218", "A382503" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-17T14:54:34
oeisdata/seq/A382/A382503.seq
99ca97a0b0c76605cd8f658aa457b5c3
A382504
Numbers k such that one or both of sigma(k) + k and sigma(k) - k is a perfect number.
[ "6", "10", "25", "28", "496", "652", "8128", "10682", "10828", "33550336", "44655764", "8589869056", "8623554304" ]
[ "nonn", "more" ]
50
1
1
[ "A000203", "A000396", "A237286", "A382504" ]
null
Leo Hennig, Mar 29 2025
2025-04-08T22:03:19
oeisdata/seq/A382/A382504.seq
9a80e90a952394836e4ed508fb5e75d2
A382505
a(n) is the number of distinct numbers of diagonal transversals in Brown's diagonal Latin squares of order 2n.
[ "0", "1", "2", "20", "349" ]
[ "nonn", "more", "hard" ]
8
1
3
[ "A339641", "A344105", "A381971", "A382505" ]
null
Eduard I. Vatutin, Mar 29 2025
2025-04-03T21:22:41
oeisdata/seq/A382/A382505.seq
5ac5e790bf8e336ac395e6c11203b926
A382506
a(n) is the smallest k such that sigma(n) + k is a perfect number.
[ "5", "3", "2", "21", "0", "16", "20", "13", "15", "10", "16", "0", "14", "4", "4", "465", "10", "457", "8", "454", "464", "460", "4", "436", "465", "454", "456", "440", "466", "424", "464", "433", "448", "442", "448", "405", "458", "436", "440", "406", "454", "400", "452", "412", "418", "424", "448", "372", "439", "403", "424", "398", "442", "376", "424", "376", "416", "406", "436", "328", "434", "400" ]
[ "nonn" ]
55
1
1
[ "A000203", "A000396", "A081357", "A146542", "A382506", "A382929" ]
null
Leo Hennig, Mar 29 2025
2025-04-12T09:43:49
oeisdata/seq/A382/A382506.seq
f6577c0780b65fc556d9a63f3d747f73
A382507
Number of half turn symmetric lattice congruences of the weak order on the symmetric group S_n.
[ "1", "2", "3", "16", "66", "13726", "11547029" ]
[ "nonn", "more" ]
4
1
2
[ "A091687", "A382507" ]
null
Ludovic Schwob, Mar 30 2025
2025-04-04T22:46:08
oeisdata/seq/A382/A382507.seq
61375cc9e3f28764245ce49e069fbd65
A382508
a(n) is the number of solutions to the problem described in A381621 with smallest price equal to n.
[ "4728", "2314", "1165", "2169", "1429", "703", "304", "1006", "283", "1532", "129", "351", "135", "241", "595", "668", "58", "175", "72", "511", "60", "136", "52", "166", "994", "51", "36", "110", "35", "331", "15", "123", "12", "49", "109", "69", "20", "39", "12", "301", "18", "36", "20", "37", "57", "31", "19", "74", "6", "315", "11", "29", "8", "10", "38", "24", "10", "25", "6", "95" ]
[ "nonn", "fini", "full" ]
11
1
1
[ "A381619", "A381620", "A381621", "A382508" ]
null
Hugo Pfoertner, Mar 30 2025
2025-03-31T08:59:09
oeisdata/seq/A382/A382508.seq
53a06a7c3352292e2a9f3a258146b41c
A382509
Integers s = (p1+p2)/4 such that p1 and p2 are consecutive primes and s can be written in the form p*2^k with k>=0 and p>2 prime.
[ "3", "6", "13", "17", "28", "38", "43", "67", "80", "88", "96", "118", "127", "137", "167", "178", "188", "193", "218", "223", "272", "283", "298", "302", "328", "368", "472", "487", "508", "563", "592", "613", "617", "634", "643", "647", "662", "718", "773", "778", "802", "808", "872", "878", "932", "1033", "1142", "1168", "1172", "1187", "1193", "1198", "1256", "1277" ]
[ "nonn", "easy" ]
21
1
1
[ "A001043", "A118134", "A382509" ]
null
Karl-Heinz Hofmann and Hugo Pfoertner, Apr 18 2025
2025-04-21T13:23:55
oeisdata/seq/A382/A382509.seq
5ce5378b28cab5aa479efad41e4622ba
A382510
a(n) is the number of solutions to the "sum equals product" riddle with n prices v_j, i.e., find positive integers v_j, v_{j+1}>=v_j such that 100^(n-1)*Sum_{k=1..n} v_k = Product_{k=1..n} v_k.
[ "1", "13", "622", "22640" ]
[ "nonn", "bref", "hard", "more" ]
6
1
2
[ "A380887", "A381619", "A381620", "A381621", "A382508", "A382510" ]
null
Hugo Pfoertner, Apr 01 2025
2025-04-01T21:37:34
oeisdata/seq/A382/A382510.seq
25e0459d8c93ec0d2ce0912586dda3a5
A382511
Expansion of Sum_{p prime} x^p / (1 - x^p)^3.
[ "0", "1", "1", "3", "1", "9", "1", "10", "6", "18", "1", "31", "1", "31", "21", "36", "1", "66", "1", "65", "34", "69", "1", "114", "15", "94", "45", "115", "1", "196", "1", "136", "72", "156", "43", "249", "1", "193", "97", "246", "1", "357", "1", "263", "165", "279", "1", "436", "28", "380", "159", "361", "1", "549", "81", "442", "196", "438", "1", "753", "1", "499", "276", "528", "106" ]
[ "nonn" ]
4
1
4
[ "A000217", "A001221", "A007437", "A069359", "A305614", "A322078", "A382511" ]
null
Ilya Gutkovskiy, Mar 30 2025
2025-04-04T22:45:26
oeisdata/seq/A382/A382511.seq
57b3f8f0a6591b1111613dc614ce23dc
A382512
Expansion of Sum_{p prime} x^p / (1 - x^p)^p.
[ "0", "1", "1", "2", "1", "6", "1", "4", "6", "10", "1", "16", "1", "14", "30", "8", "1", "30", "1", "45", "56", "22", "1", "48", "70", "26", "45", "98", "1", "196", "1", "16", "132", "34", "420", "96", "1", "38", "182", "350", "1", "588", "1", "308", "615", "46", "1", "160", "924", "740", "306", "481", "1", "198", "2002", "1744", "380", "58", "1", "1605", "1", "62", "3234", "32", "3640" ]
[ "nonn" ]
4
1
4
[ "A001221", "A069359", "A157019", "A322078", "A373458", "A373459", "A382512" ]
null
Ilya Gutkovskiy, Mar 30 2025
2025-04-04T22:45:35
oeisdata/seq/A382/A382512.seq
44eb717b093943443c6f63280025fc0b
A382513
Expansion of Sum_{p prime} p * x^p / (1 - p * x^p).
[ "0", "2", "3", "4", "5", "17", "7", "16", "27", "57", "11", "145", "13", "177", "368", "256", "17", "1241", "19", "1649", "2530", "2169", "23", "10657", "3125", "8361", "19683", "18785", "29", "107442", "31", "65536", "178478", "131361", "94932", "793585", "37", "524649", "1596520", "1439201", "41", "6997770", "43", "4208945", "16302032" ]
[ "nonn" ]
4
1
2
[ "A008472", "A055225", "A069359", "A373458", "A373459", "A382513" ]
null
Ilya Gutkovskiy, Mar 30 2025
2025-04-04T22:44:56
oeisdata/seq/A382/A382513.seq
2f935f3a828d2f58d7c66bcc84380e82
A382514
Expansion of 1/(1 - x/(1 - 4*x)^(3/2)).
[ "1", "1", "7", "43", "255", "1493", "8695", "50517", "293163", "1700335", "9859019", "57156631", "331332423", "1920621431", "11132911939", "64531189379", "374047777319", "2168115796941", "12567146992975", "72843402779669", "422224417571347", "2447350774345341", "14185640454054279", "82224565359415849" ]
[ "nonn", "easy" ]
18
0
3
[ "A002457", "A026671", "A382514", "A382515" ]
null
Seiichi Manyama, Mar 30 2025
2025-04-09T23:40:05
oeisdata/seq/A382/A382514.seq
b1e5b089908043cea900ca86eb8ec3f5
A382515
Expansion of 1/(1 - x/(1 - 4*x)^(5/2)).
[ "1", "1", "11", "91", "691", "5101", "37323", "272405", "1987047", "14493479", "105718071", "771148119", "5625136651", "41032826127", "299316769887", "2183389173811", "15926906427179", "116180104751925", "847485191674867", "6182049517420133", "45095462188117951", "328952511222499589", "2399570809473795931" ]
[ "nonn", "easy" ]
19
0
3
[ "A002802", "A026671", "A382514", "A382515" ]
null
Seiichi Manyama, Mar 30 2025
2025-03-31T07:09:48
oeisdata/seq/A382/A382515.seq
a32df15cef91f26d9a012adc7d0f17c7