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int64
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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A363701
Numbers k with the property that the character table of S_k contains a zero in every nontrivial column.
[ "0", "1", "5", "6", "8", "9", "10", "12", "14", "17", "21", "28", "30", "32", "34", "36", "37" ]
[ "nonn", "more", "hard" ]
34
1
3
[ "A000217", "A010054", "A175595", "A260682", "A363675", "A363676", "A363701" ]
null
Diego Martin Duro, Jun 16 2023
2024-11-17T07:31:37
oeisdata/seq/A363/A363701.seq
da5714b0c15f2b71da292dac75305398
A363702
Let m be the least integer for which there exists a strictly increasing sequence u of n integers in {1..m} such that x = (2 * Sum_{k=1..n} k*prime(u(k))) / (n*(n+1)) is an integer. a(n) is the least x, or -1 if no such integer x exists.
[ "2", "4", "11", "12", "12", "12", "16", "21", "24", "22", "24", "31", "32", "34", "41", "40", "42", "44", "49", "50", "52", "52", "61", "63", "62", "68", "70", "75", "74", "82", "88", "89", "92", "92", "102", "106", "106", "106", "113", "118", "118", "118", "125", "127", "132", "132", "141", "148", "142", "150", "154", "158", "158", "162", "171", "175", "172", "178", "181", "187" ]
[ "nonn" ]
68
1
1
[ "A045345", "A050248", "A363702" ]
null
Jean-Marc Rebert, Jun 16 2023
2023-09-06T21:20:53
oeisdata/seq/A363/A363702.seq
daea4c2cae94fe479403ef41e6c95289
A363703
Lower independence number of the n-folded cube graph.
[ "1", "1", "4", "4", "6", "8", "24", "32" ]
[ "nonn", "more" ]
30
2
3
null
null
Eric W. Weisstein, Aug 02 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363703.seq
8ebf618cc2ee7aa5487426ff91b14b8f
A363704
Decimal expansion of lim_{x -> infinity} ((Sum_{k>=1} (k^(1/k^(1 + 1/x)) - 1)) - x^2).
[ "9", "8", "8", "5", "4", "9", "6", "0", "1", "1", "4", "2", "2", "6", "8", "7", "5", "0", "6", "4", "4", "7", "5", "4", "1", "0", "8", "3", "3", "9", "9", "7", "1", "2", "6", "4", "4", "2", "1", "9", "9", "8", "6", "8", "3", "8", "0", "1", "5", "2", "3", "8", "8", "1", "7", "3", "5", "4", "3", "0", "7", "0", "6", "7", "9", "5", "2", "2", "3", "5", "4", "8", "4", "9", "2", "9", "2", "2", "1", "6", "2", "6", "9", "5", "3", "2", "6" ]
[ "nonn", "cons" ]
26
0
1
[ "A001620", "A098572", "A329117", "A350862", "A351885", "A363704", "A363716" ]
null
Daniel Hoyt, Jun 16 2023
2023-06-18T10:04:47
oeisdata/seq/A363/A363704.seq
d428b8e699dc9f309ba6a3854d6a9dc3
A363705
The minimum irregularity of all maximal 2-degenerate graphs with n vertices.
[ "0", "4", "2", "6", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8" ]
[ "nonn", "easy" ]
21
3
2
[ "A002378", "A028896", "A046092", "A363705" ]
null
Allan Bickle, Jun 16 2023
2024-07-16T14:24:35
oeisdata/seq/A363/A363705.seq
3a415eb3886bb24e7314233f4e86547b
A363706
a(n) is the sigma irregularity of the n-th power of a path graph of length at least 3*n.
[ "2", "14", "52", "140", "310", "602", "1064", "1752", "2730", "4070", "5852", "8164", "11102", "14770", "19280", "24752", "31314", "39102", "48260", "58940", "71302", "85514", "101752", "120200", "141050", "164502", "190764", "220052", "252590", "288610", "328352", "372064", "420002", "472430", "529620", "591852", "659414", "732602", "811720", "897080", "989002" ]
[ "nonn", "easy" ]
21
1
1
[ "A006325", "A011379", "A181617", "A270205", "A363706" ]
null
Allan Bickle, Jun 16 2023
2024-02-19T01:35:43
oeisdata/seq/A363/A363706.seq
07e6196317a0701a3d40ea2435572cf0
A363707
For n >= 2, a(n) = a(n-1) + a(n-2) + A051697(n), a(0)=0, a(1)=1.
[ "0", "1", "3", "7", "13", "25", "43", "75", "125", "207", "343", "561", "915", "1489", "2417", "3919", "6353", "10289", "16659", "26967", "43645", "70631", "114299", "184953", "299275", "484251", "783549", "1267829", "2051407", "3319265", "5370701", "8689997", "14060729", "22750757", "36811517", "59562311", "96373865", "155936213", "252310115" ]
[ "nonn" ]
23
0
3
[ "A051697", "A363707" ]
null
Yanick Willert, Jun 16 2023
2023-08-02T12:01:09
oeisdata/seq/A363/A363707.seq
221c7d5b96d383b130217c0c25136c3c
A363708
Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) terms, with pairs numbered according to the position of the first term in the pair.
[ "1", "2", "1", "3", "2", "3", "4", "5", "2", "4", "6", "5", "7", "2", "5", "4", "8", "7", "9", "10", "2", "4", "10", "11", "8", "12", "2", "10", "13", "14", "15", "13", "11", "12", "14", "16", "2", "17", "10", "2", "18", "15", "12", "13", "19", "20", "21", "14", "17", "22", "23", "17", "10", "24", "2", "13", "12", "15", "20", "12", "25", "21", "17", "26", "14", "27", "28", "22", "29", "30", "31", "32" ]
[ "nonn" ]
29
1
2
[ "A026272", "A363654", "A363708", "A363757" ]
null
Neal Gersh Tolunsky, Jun 16 2023
2023-06-29T13:21:14
oeisdata/seq/A363/A363708.seq
51a1edeb09f87ad05b7753ee8830e35b
A363709
For n >= 0, a(n) is the least integer i >= 0 such that n + (n + 1) + ... + (n + i) is a prime number or a(n) = -1 if no such i exists.
[ "2", "1", "0", "0", "-1", "0", "1", "0", "1", "1", "-1", "0", "-1", "0", "1", "1", "-1", "0", "1", "0", "1", "1", "-1", "0", "-1", "-1", "1", "-1", "-1", "0", "1", "0", "-1", "1", "-1", "1", "1", "0", "-1", "1", "-1", "0", "-1", "0", "1", "-1", "-1", "0", "1", "-1", "1", "1", "-1", "0", "1", "-1", "1", "-1", "-1", "0", "-1", "0", "-1", "1", "-1", "1", "-1", "0", "1", "1", "-1", "0", "-1", "0", "1", "1", "-1", "-1", "1", "0", "-1" ]
[ "sign" ]
11
0
1
[ "A000040", "A005384", "A053176", "A067812", "A077654", "A363709" ]
null
Ctibor O. Zizka, Jun 17 2023
2023-07-06T22:06:20
oeisdata/seq/A363/A363709.seq
aa9ac080f55e48151e22678c5f5e106f
A363710
a(n) is the number of pairs of nonnegative integers (x, y) such that x + y = n and A003188(x) AND A003188(y) = 0 (where AND denotes the bitwise AND operator).
[ "1", "2", "2", "2", "4", "4", "2", "2", "4", "8", "6", "4", "6", "4", "2", "2", "4", "8", "10", "8", "12", "12", "6", "4", "6", "12", "8", "4", "6", "4", "2", "2", "4", "8", "10", "8", "16", "20", "10", "8", "12", "24", "20", "12", "16", "12", "6", "4", "6", "12", "16", "12", "16", "16", "8", "4", "6", "12", "8", "4", "6", "4", "2", "2", "4", "8", "10", "8", "16", "20", "10", "8", "16", "32", "28", "20", "28" ]
[ "nonn", "base" ]
11
0
2
[ "A003188", "A075427", "A332497", "A332498", "A363710" ]
null
Rémy Sigrist, Jun 17 2023
2025-06-02T16:49:53
oeisdata/seq/A363/A363710.seq
18f5deaab78cc4d9c86e90c2d2b1a222
A363711
Number of ways to write n as sum of a positive square and a positive fourth power.
[ "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "0", "1" ]
[ "nonn", "easy" ]
12
1
17
[ "A010052", "A063725", "A078359", "A111925", "A363711", "A363713", "A363714" ]
null
Seiichi Manyama, Jun 17 2023
2023-06-17T10:01:47
oeisdata/seq/A363/A363711.seq
bca3257a648832331a1a376dc5202751
A363712
Number of ways to write n as sum of a positive cube and a positive fourth power.
[ "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "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", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "easy" ]
12
1
null
[ "A010057", "A100291", "A217196", "A280618", "A363711", "A363712" ]
null
Seiichi Manyama, Jun 17 2023
2023-06-17T10:01:29
oeisdata/seq/A363/A363712.seq
9b8b08e0e56a3266c7f7ccaef2025505
A363713
Number of ways to write n as sum of a positive square and a positive fifth power.
[ "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn", "easy" ]
10
1
null
[ "A010052", "A063725", "A078359", "A100292", "A363711", "A363713", "A363715" ]
null
Seiichi Manyama, Jun 17 2023
2023-06-17T10:01:42
oeisdata/seq/A363/A363713.seq
eca556f33e46ba305d2f06cbddb9a073
A363714
Numbers that are the sum of a positive square and a positive fourth power in more than one way.
[ "17", "65", "82", "97", "145", "257", "272", "305", "337", "377", "442", "481", "545", "626", "641", "706", "785", "881", "1025", "1040", "1105", "1297", "1312", "1345", "1377", "1525", "1552", "1780", "1850", "1921", "1937", "2225", "2320", "2385", "2402", "2417", "2465", "2482", "2501", "2657", "2977", "3026", "3505", "3697", "3737", "3845", "4097", "4100", "4105", "4112", "4177", "4225", "4321" ]
[ "nonn" ]
9
1
1
[ "A111925", "A363711", "A363714" ]
null
Seiichi Manyama, Jun 17 2023
2023-06-17T10:01:38
oeisdata/seq/A363/A363714.seq
75f776e5da574b64d916bbe5fe5f6344
A363715
Numbers that are the sum of a positive square and a positive fifth power in more than one way.
[ "257", "1025", "1553", "1924", "2705", "4388", "6725", "7812", "11225", "11268", "12132", "15908", "18801", "19012", "20407", "23652", "28225", "28256", "29585", "32432", "32793", "33057", "33857", "35001", "36132", "36249", "36368", "37124", "37668", "42372", "48985", "52932", "59050", "59305", "60073", "62033", "62532", "78993", "79424", "83393", "87057", "91810" ]
[ "nonn" ]
7
1
1
[ "A100292", "A363713", "A363715" ]
null
Seiichi Manyama, Jun 17 2023
2023-06-17T10:01:33
oeisdata/seq/A363/A363715.seq
929dd04c86393732ad337128ffb2399c
A363716
Decimal expansion of Sum_{k>=2} (1/k!) * k-th derivative of zeta(k).
[ "9", "3", "6", "1", "9", "1", "3", "1", "9", "4", "0", "4", "4", "8", "7", "0", "5", "1", "6", "4", "1", "1", "9", "2", "0", "3", "4", "8", "0", "3", "1", "3", "4", "4", "8", "8", "2", "4", "7", "6", "7", "0", "6", "2", "7", "4", "0", "7", "2", "8", "3", "2", "7", "8", "8", "4", "3", "6", "1", "1", "9", "4", "5", "9", "9", "5", "8", "4", "7", "1", "7", "8", "9", "1", "6", "3", "7", "0", "0", "5", "6", "4", "9", "3", "3", "6", "3", "3", "8", "3", "9", "6", "2", "3", "6", "1", "1", "4", "5", "7", "2", "4", "8", "0", "2", "4" ]
[ "nonn", "cons" ]
14
0
1
[ "A098572", "A363704", "A363716" ]
null
Vaclav Kotesovec, Jun 17 2023
2023-06-18T11:41:29
oeisdata/seq/A363/A363716.seq
d7feeab3de9d946b0cac5c24c7b15afd
A363717
Prime radicands p == 1 (mod 9) of pure cubic number fields of type Gamma.
[ "541", "919", "1279", "1531", "2161", "2269", "3637", "6211", "6427", "7129", "7723", "7867", "7993", "8389", "8461", "9649", "9901", "10009", "11071", "13627", "15031", "15391", "15607", "15661", "15787", "16741", "17713", "17911", "17929" ]
[ "nonn", "more" ]
32
1
1
[ "A061237", "A363699", "A363717" ]
null
Daniel Constantin Mayer, Jun 17 2023
2025-01-08T12:49:03
oeisdata/seq/A363/A363717.seq
7bda650337eaadc21e20c85e2d662a07
A363718
Irregular triangle read by rows. An infinite binary tree which has root node 1 in row n = 0. Each node then has left child m-1 if greater than 0 and right child m+1, where m is the value of the parent node.
[ "1", "2", "1", "3", "2", "2", "4", "1", "3", "1", "3", "3", "5", "2", "2", "4", "2", "2", "4", "2", "4", "4", "6", "1", "3", "1", "3", "3", "5", "1", "3", "1", "3", "3", "5", "1", "3", "3", "5", "3", "5", "5", "7", "2", "2", "4", "2", "2", "4", "2", "4", "4", "6", "2", "2", "4", "2", "2", "4", "2", "4", "4", "6", "2", "2", "4", "2", "4", "4", "6", "2", "4", "4", "6", "4", "6", "6", "8", "1", "3", "1", "3", "3", "5", "1", "3", "1" ]
[ "nonn", "easy", "tabf" ]
42
0
2
[ "A000079", "A000108", "A001405", "A007001", "A053121", "A173258", "A363718", "A367508", "A367951", "A367953" ]
null
John Tyler Rascoe, Jun 17 2023
2024-09-20T06:09:35
oeisdata/seq/A363/A363718.seq
c0e669501be5eb801fcb3e76f8af4317
A363719
Number of integer partitions of n satisfying (mean) = (median) = (mode), assuming there is a unique mode.
[ "1", "2", "2", "3", "2", "4", "2", "5", "3", "5", "2", "10", "2", "7", "7", "12", "2", "18", "2", "24", "16", "13", "2", "58", "15", "18", "37", "60", "2", "123", "2", "98", "79", "35", "103", "332", "2", "49", "166", "451", "2", "515", "2", "473", "738", "92", "2", "1561", "277", "839", "631", "1234", "2", "2043", "1560", "2867", "1156", "225", "2", "9020" ]
[ "nonn" ]
19
1
2
[ "A000009", "A000041", "A008284", "A008289", "A027193", "A237984", "A240219", "A325347", "A326567", "A326568", "A327472", "A359889", "A359890", "A359893", "A359894", "A359895", "A359896", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359909", "A359910", "A362608", "A363719", "A363720", "A363721", "A363722", "A363723", "A363724", "A363725", "A363726", "A363727", "A363728", "A363729", "A363730", "A363731", "A363740", "A363741", "A363742" ]
null
Gus Wiseman, Jun 19 2023
2023-06-22T18:45:00
oeisdata/seq/A363/A363719.seq
f21db7e6699516d60965a382eeba458a
A363720
Number of integer partitions of n with different mean, median, and mode.
[ "0", "0", "0", "0", "0", "0", "0", "2", "3", "5", "7", "16", "17", "34", "38", "50", "79", "115", "123", "198", "220", "291", "399", "536", "605", "815", "1036", "1241", "1520", "2059", "2315", "3132", "3708", "4491", "5668", "6587", "7788", "10259", "12299", "14515", "17153", "21558", "24623", "30876", "35540", "41476", "52023", "61931", "70811", "85545" ]
[ "nonn" ]
9
0
8
[ "A000009", "A000041", "A008284", "A008289", "A027193", "A237984", "A240219", "A325347", "A326567", "A326568", "A327472", "A359889", "A359890", "A359893", "A359894", "A359895", "A359896", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359909", "A359910", "A362608", "A363719", "A363720", "A363721", "A363723", "A363724", "A363725", "A363726", "A363727", "A363728", "A363730", "A363731", "A363740", "A363741", "A363742" ]
null
Gus Wiseman, Jun 21 2023
2023-06-22T23:34:54
oeisdata/seq/A363/A363720.seq
f4f658edecb8db7b6b28c0961e2ec448
A363721
Number of odd-length integer partitions of n satisfying (mean) = (median) = (mode), assuming there is a unique mode.
[ "1", "1", "2", "1", "2", "2", "2", "1", "3", "3", "2", "2", "2", "5", "7", "1", "2", "8", "2", "9", "16", "11", "2", "2", "15", "16", "37", "33", "2", "44", "2", "1", "79", "33", "103", "127", "2", "47", "166", "39", "2", "214", "2", "384", "738", "90", "2", "2", "277", "185", "631", "1077", "2", "1065", "1560", "477", "1156", "223", "2", "2863" ]
[ "nonn" ]
7
1
3
[ "A000009", "A000041", "A008284", "A008289", "A027193", "A237984", "A240219", "A325347", "A326567", "A326568", "A327472", "A359893", "A359894", "A359895", "A359896", "A359899", "A359900", "A359901", "A359902", "A359910", "A362608", "A363719", "A363720", "A363721", "A363726", "A363727", "A363728", "A363740", "A363741" ]
null
Gus Wiseman, Jun 21 2023
2023-06-22T23:34:48
oeisdata/seq/A363/A363721.seq
ee354f5e5ac8dd40a2c7f33ad5f3bed9
A363722
Nonprime numbers whose prime indices satisfy (mean) = (median) = (mode), assuming there is a unique mode.
[ "4", "8", "9", "16", "25", "27", "32", "49", "64", "81", "90", "121", "125", "128", "169", "243", "256", "270", "289", "343", "361", "512", "525", "529", "550", "625", "729", "756", "810", "841", "961", "1024", "1331", "1369", "1666", "1681", "1849", "1911", "1950", "2048", "2187", "2197", "2209", "2268", "2401", "2430", "2625", "2695", "2700", "2750", "2809" ]
[ "nonn" ]
5
1
1
[ "A000961", "A001222", "A056239", "A112798", "A240219", "A326567", "A326568", "A327473", "A327476", "A356862", "A359178", "A359889", "A359890", "A359893", "A359894", "A359908", "A360005", "A360009", "A360550", "A362608", "A362610", "A362611", "A362613", "A362614", "A362615", "A363486", "A363487", "A363719", "A363720", "A363721", "A363722", "A363723", "A363724", "A363725", "A363727", "A363728", "A363729", "A363730", "A363731", "A363740", "A363741" ]
null
Gus Wiseman, Jun 24 2023
2023-06-24T07:56:08
oeisdata/seq/A363/A363722.seq
58ee1ffa9f429be287845cface235644
A363723
Number of integer partitions of n having a unique mode equal to the mean, i.e., partitions whose mean appears more times than each of the other parts.
[ "0", "1", "2", "2", "3", "2", "4", "2", "5", "3", "5", "2", "10", "2", "7", "7", "12", "2", "18", "2", "24", "16", "13", "2", "60", "15", "18", "37", "60", "2", "129", "2", "104", "80", "35", "104", "352", "2", "49", "168", "501", "2", "556", "2", "489", "763", "92", "2", "1799", "292", "985", "649", "1296", "2", "2233", "1681", "3379", "1204", "225", "2", "10661" ]
[ "nonn" ]
7
0
3
[ "A000009", "A000041", "A008284", "A008289", "A237984", "A240219", "A325347", "A326567", "A326568", "A327472", "A327473", "A327476", "A359889", "A359893", "A359901", "A362562", "A362608", "A363719", "A363720", "A363723", "A363724", "A363725", "A363727", "A363730", "A363731", "A363740" ]
null
Gus Wiseman, Jun 24 2023
2023-06-25T08:11:28
oeisdata/seq/A363/A363723.seq
b1e9f23e1fcf07855000d56c913d96e7
A363724
Number of integer partitions of n whose mean is a mode, i.e., partitions whose mean appears at least as many times as each of the other parts.
[ "1", "2", "2", "3", "2", "5", "2", "5", "5", "6", "2", "15", "2", "8", "15", "17", "2", "30", "2", "43", "30", "15", "2", "112", "36", "21", "60", "119", "2", "251", "2", "201", "126", "41", "271", "655", "2", "57", "250", "1060", "2", "1099", "2", "844", "1508", "107", "2", "3484", "802", "2068", "900", "2136", "2", "4558", "3513", "7071", "1630", "259", "2", "20260" ]
[ "nonn" ]
8
1
2
[ "A000009", "A000041", "A008284", "A008289", "A237984", "A240219", "A326567", "A326568", "A327472", "A362562", "A362608", "A363719", "A363720", "A363723", "A363724", "A363725", "A363726", "A363727", "A363728", "A363730", "A363731", "A363740" ]
null
Gus Wiseman, Jun 24 2023
2023-06-25T18:20:23
oeisdata/seq/A363/A363724.seq
d083069bc87acc7047e0a2dc7551a94c
A363725
Number of integer partitions of n with a different mean, median, and mode, assuming there is a unique mode.
[ "0", "0", "0", "0", "0", "0", "0", "1", "1", "3", "3", "8", "8", "17", "19", "28", "39", "59", "68", "106", "123", "165", "220", "301", "361", "477", "605", "745", "929", "1245", "1456", "1932", "2328", "2846", "3590", "4292", "5111", "6665", "8040", "9607", "11532", "14410", "16699", "20894", "24287", "28706", "35745", "42845", "49548", "59963", "70985" ]
[ "nonn" ]
9
0
10
[ "A000009", "A000041", "A008284", "A008289", "A237984", "A240219", "A325347", "A325695", "A326567", "A326568", "A327472", "A359893", "A359894", "A359896", "A359900", "A359901", "A359902", "A362608", "A363719", "A363720", "A363723", "A363725", "A363727", "A363728", "A363730" ]
null
Gus Wiseman, Jun 22 2023
2023-06-23T23:29:30
oeisdata/seq/A363/A363725.seq
995d7c58b5712f88bec42f890a8bfa53
A363726
Number of odd-length integer partitions of n with a unique mode.
[ "0", "1", "1", "2", "2", "4", "4", "7", "8", "12", "14", "22", "26", "39", "50", "67", "86", "118", "148", "196", "245", "315", "394", "507", "629", "792", "979", "1231", "1503", "1873", "2286", "2814", "3424", "4194", "5073", "6183", "7449", "9014", "10827", "13055", "15603", "18713", "22308", "26631", "31646", "37641", "44559", "52835", "62374", "73671" ]
[ "nonn" ]
8
0
4
[ "A000009", "A000041", "A001227", "A008284", "A008289", "A026424", "A027193", "A325347", "A356862", "A359893", "A359901", "A362608", "A363719", "A363720", "A363724", "A363725", "A363726", "A363731", "A363740" ]
null
Gus Wiseman, Jun 27 2023
2023-06-27T19:41:16
oeisdata/seq/A363/A363726.seq
035c84b7f3ec255bbd91c13d9ddb073c
A363727
Numbers whose prime indices satisfy (mean) = (median) = (mode), assuming there is a unique mode.
[ "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "23", "25", "27", "29", "31", "32", "37", "41", "43", "47", "49", "53", "59", "61", "64", "67", "71", "73", "79", "81", "83", "89", "90", "97", "101", "103", "107", "109", "113", "121", "125", "127", "128", "131", "137", "139", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193", "197", "199" ]
[ "nonn" ]
5
1
1
[ "A001222", "A056239", "A112798", "A215366", "A240219", "A326567", "A326568", "A327473", "A327476", "A356862", "A359178", "A359889", "A359890", "A359893", "A359894", "A359908", "A360005", "A360009", "A360248", "A360550", "A362608", "A362610", "A362611", "A362613", "A362614", "A362615", "A363486", "A363487", "A363719", "A363720", "A363721", "A363722", "A363723", "A363724", "A363725", "A363727", "A363728", "A363729", "A363730", "A363731", "A363740", "A363741" ]
null
Gus Wiseman, Jun 23 2023
2023-06-24T07:56:17
oeisdata/seq/A363/A363727.seq
88b14ca352e730e9cccf17648655c49b
A363728
Number of integer partitions of n that are not constant but satisfy (mean) = (median) = (mode), assuming there is a unique mode.
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "4", "0", "3", "3", "7", "0", "12", "0", "18", "12", "9", "0", "50", "12", "14", "33", "54", "0", "115", "0", "92", "75", "31", "99", "323", "0", "45", "162", "443", "0", "507", "0", "467", "732", "88", "0", "1551", "274", "833", "627", "1228", "0", "2035", "1556", "2859", "1152", "221", "0", "9008", "0", "295", "4835", "5358" ]
[ "nonn" ]
9
1
12
[ "A000009", "A000041", "A008284", "A008289", "A024619", "A144300", "A237984", "A240219", "A325347", "A326567", "A326568", "A327472", "A359893", "A359894", "A359901", "A359902", "A362608", "A363719", "A363720", "A363721", "A363727", "A363728", "A363729" ]
null
Gus Wiseman, Jun 23 2023
2023-08-16T11:01:41
oeisdata/seq/A363/A363728.seq
758359a81cb87e3a3c037fb79a65d35e
A363729
Numbers that are not a power of a prime but whose prime indices satisfy (mean) = (median) = (mode), assuming there is a unique mode.
[ "90", "270", "525", "550", "756", "810", "1666", "1911", "1950", "2268", "2430", "2625", "2695", "2700", "2750", "5566", "6762", "6804", "6897", "7128", "7290", "8100", "8500", "9310", "9750", "10285", "10478", "11011", "11550", "11662", "12250", "12375", "12495", "13125", "13377", "13750", "14014", "14703", "18865", "19435", "20412", "21384" ]
[ "nonn" ]
5
1
1
[ "A000961", "A001222", "A024619", "A056239", "A112798", "A215366", "A240219", "A326567", "A326568", "A327473", "A327476", "A356862", "A359178", "A359889", "A359890", "A359893", "A359894", "A359908", "A360005", "A360009", "A360248", "A360550", "A362608", "A362610", "A362611", "A362613", "A362614", "A362615", "A363486", "A363487", "A363719", "A363720", "A363721", "A363722", "A363723", "A363724", "A363725", "A363727", "A363728", "A363729", "A363730", "A363731", "A363740", "A363741" ]
null
Gus Wiseman, Jun 24 2023
2023-06-24T07:56:13
oeisdata/seq/A363/A363729.seq
32094b5a1f52076fd19a29e8ddadeff6
A363730
Numbers whose prime indices have different mean, median, and mode.
[ "42", "60", "66", "70", "78", "84", "102", "114", "130", "132", "138", "140", "150", "154", "156", "165", "170", "174", "180", "182", "186", "190", "195", "204", "220", "222", "228", "230", "231", "246", "255", "258", "260", "266", "276", "282", "285", "286", "290", "294", "308", "310", "315", "318", "322", "330", "340", "345", "348", "354", "357", "360", "364" ]
[ "nonn" ]
5
1
1
[ "A000961", "A001222", "A056239", "A112798", "A240219", "A326567", "A326568", "A327473", "A327476", "A356862", "A359178", "A359889", "A359890", "A359894", "A359908", "A360005", "A362608", "A362610", "A362611", "A362613", "A362614", "A362615", "A363486", "A363487", "A363719", "A363720", "A363722", "A363723", "A363724", "A363725", "A363727", "A363729", "A363730", "A363731", "A363740", "A363741", "A363742" ]
null
Gus Wiseman, Jun 24 2023
2023-06-24T13:03:02
oeisdata/seq/A363/A363730.seq
0fd99e4a46de412266cc8ac134e236f2
A363731
Number of integer partitions of n whose mean is a mode but not the only mode.
[ "0", "0", "0", "0", "0", "0", "1", "0", "0", "2", "1", "0", "5", "0", "1", "8", "5", "0", "12", "0", "19", "14", "2", "0", "52", "21", "3", "23", "59", "0", "122", "0", "97", "46", "6", "167", "303", "0", "8", "82", "559", "0", "543", "0", "355", "745", "15", "0", "1685", "510", "1083", "251", "840", "0", "2325", "1832", "3692", "426", "34", "0", "9599" ]
[ "nonn" ]
8
0
10
[ "A000009", "A000041", "A008284", "A008289", "A237984", "A240219", "A326567", "A326568", "A327472", "A327473", "A327476", "A356862", "A359893", "A362562", "A362608", "A363719", "A363720", "A363723", "A363724", "A363725", "A363727", "A363731", "A363740" ]
null
Gus Wiseman, Jun 24 2023
2023-06-25T18:20:17
oeisdata/seq/A363/A363731.seq
457732740e6585025c71cad4f6557238
A363732
Triangle read by rows. The triangle algorithm applied to (-1)^n/n!.
[ "1", "-2", "1", "5", "-4", "1", "-15", "15", "-6", "1", "52", "-60", "30", "-8", "1", "-203", "260", "-150", "50", "-10", "1", "877", "-1218", "780", "-300", "75", "-12", "1", "-4140", "6139", "-4263", "1820", "-525", "105", "-14", "1", "21147", "-33120", "24556", "-11368", "3640", "-840", "140", "-16", "1", "-115975", "190323", "-149040", "73668", "-25578", "6552", "-1260", "180", "-18", "1" ]
[ "sign", "tabl" ]
21
0
2
[ "A000012", "A000079", "A000110", "A000670", "A005493", "A007318", "A011971", "A011972", "A023531", "A027642", "A056857", "A122045", "A123346", "A153641", "A154921", "A155585", "A164555", "A196838", "A196839", "A293037", "A363524", "A363732" ]
null
Peter Luschny, Jun 18 2023
2023-07-30T19:49:27
oeisdata/seq/A363/A363732.seq
e70e072beaafb4ec99d4baabd2d8542e
A363733
Array read by upwards antidiagonals. The family of polynomials generated by the divisibility matrix (A113704) evaluated over the nonnegative integers.
[ "1", "0", "1", "0", "1", "1", "0", "2", "2", "1", "0", "2", "6", "3", "1", "0", "3", "10", "12", "4", "1", "0", "2", "22", "30", "20", "5", "1", "0", "4", "34", "93", "68", "30", "6", "1", "0", "2", "78", "246", "276", "130", "42", "7", "1", "0", "4", "130", "768", "1028", "655", "222", "56", "8", "1", "0", "3", "278", "2190", "4180", "3130", "1338", "350", "72", "9", "1" ]
[ "nonn", "tabl" ]
24
0
8
[ "A000005", "A001477", "A002378", "A034262", "A055895", "A066108", "A113704", "A113705", "A131471", "A190578", "A363421", "A363733", "A363734", "A363735", "A363912", "A363913" ]
null
Peter Luschny, Jun 27 2023
2025-03-23T11:17:38
oeisdata/seq/A363/A363733.seq
bde022b59b79c16cd906443cd3f77c61
A363734
a(n) = Sum_{k=0..n} n^divides(k, n), where divides(k, n) = 1 if k divides n, otherwise 0.
[ "0", "2", "5", "8", "14", "14", "27", "20", "37", "34", "47", "32", "79", "38", "67", "72", "92", "50", "121", "56", "135", "102", "107", "68", "209", "98", "127", "132", "191", "86", "263", "92", "219", "162", "167", "172", "352", "110", "187", "192", "353", "122", "371", "128", "303", "310", "227", "140", "519", "194", "345", "252", "359", "158", "479", "272", "497" ]
[ "nonn" ]
26
0
2
[ "A000005", "A113704", "A363421", "A363734", "A363735" ]
null
Peter Luschny, Jun 27 2023
2024-09-20T14:41:50
oeisdata/seq/A363/A363734.seq
e3021e800080c2d50cb0617532914e1e
A363735
a(n) = Sum_{k=0..n} n^notdivides(k, n), where notdivides(k, n) = 0 if k divides n, otherwise 1.
[ "1", "2", "4", "8", "11", "22", "22", "44", "44", "66", "74", "112", "90", "158", "158", "184", "197", "274", "240", "344", "306", "382", "422", "508", "416", "578", "602", "652", "650", "814", "698", "932", "870", "994", "1058", "1124", "1017", "1334", "1334", "1408", "1328", "1642", "1478", "1808", "1722", "1806", "1982", "2164", "1882", "2306", "2256", "2452" ]
[ "nonn" ]
22
0
2
[ "A000005", "A113704", "A363421", "A363734", "A363735" ]
null
Peter Luschny, Jun 27 2023
2023-08-06T17:51:08
oeisdata/seq/A363/A363735.seq
00b9649ca2c3efec624579da9a327b6c
A363736
a(n) = (n-1)! * Sum_{d|n} (-1)^(d+1) / (d-1)!.
[ "1", "0", "3", "-1", "25", "59", "721", "-841", "60481", "15119", "3628801", "12972959", "479001601", "8648639", "134399865601", "-218205187201", "20922789888001", "174888473759999", "6402373705728001", "-15205972772390401", "3652732042831872001", "14079294028799", "1124000727777607680001" ]
[ "sign" ]
17
1
3
[ "A087906", "A132960", "A352013", "A363736", "A363737" ]
null
Seiichi Manyama, Jun 18 2023
2023-07-03T00:53:22
oeisdata/seq/A363/A363736.seq
fc4acb9b048a6faa550e408b6b10a5db
A363737
a(n) = n! * Sum_{d|n} (-1)^(d+1) / (d! * (n/d)!).
[ "1", "0", "2", "-6", "2", "0", "2", "-1680", "10082", "0", "2", "-665280", "2", "0", "3632428802", "-36843206400", "2", "0", "2", "-670442572800", "3379030566912002", "0", "2", "-71812452903064473600", "1077167364120207360002", "0", "10002268381116211200002", "-3497296636753920000", "2", "0", "2" ]
[ "sign" ]
15
1
3
[ "A121860", "A132962", "A363736", "A363737" ]
null
Seiichi Manyama, Jun 18 2023
2023-07-03T01:00:25
oeisdata/seq/A363/A363737.seq
49014f3207aab30575aafcb8b5b4e150
A363738
Number of ordered partitions of n into cubes > 1.
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "2", "0", "0", "0", "0", "1", "0", "0", "3", "0", "0", "0", "0", "1", "0", "0", "4", "0", "0", "1", "0", "1", "0", "0", "5", "0", "0", "3", "0", "2", "0", "0", "6", "0", "0", "6", "0", "3", "0", "0", "7", "0", "0", "10", "0", "4", "1", "0", "8", "0", "0", "15", "0", "5", "4", "0", "11", "0", "0", "21", "0", "6", "10", "0", "16", "0", "0", "28", "0", "7", "20", "0", "23" ]
[ "nonn" ]
19
0
36
[ "A000578", "A010057", "A023358", "A278929", "A280542", "A363738" ]
null
Seiichi Manyama, Jun 18 2023
2023-06-20T10:02:44
oeisdata/seq/A363/A363738.seq
05fe6cefa08f323f9adaa5a137505abf
A363739
a(n) is the length of the n-th run of identical terms of A349509.
[ "2", "1", "5", "1", "17", "1", "2", "1", "5", "1", "17", "1", "26", "1", "2", "1", "23", "1", "8", "1", "44", "1", "80", "1", "2", "1", "5", "1", "17", "1", "53", "1", "26", "1", "134", "1", "80", "1", "29", "1", "23", "1", "107", "1", "2", "1", "5", "1", "71", "1", "161", "1", "2", "1", "77", "1", "35", "1", "65", "1", "59", "1", "164", "1", "26", "1", "50", "1", "8", "1", "233", "1", "194", "1", "290", "1", "2" ]
[ "nonn" ]
34
1
1
[ "A349509", "A349929", "A363739" ]
null
Stefano Spezia, Jun 19 2023
2023-08-08T09:13:08
oeisdata/seq/A363/A363739.seq
e144f5bd02ebb382d7205a77b8a6b6dc
A363740
Number of integer partitions of n whose median appears more times than any other part, i.e., partitions containing a unique mode equal to the median.
[ "1", "2", "2", "4", "5", "7", "10", "15", "18", "26", "35", "46", "61", "82", "102", "136", "174", "224", "283", "360", "449", "569", "708", "883", "1089", "1352", "1659", "2042", "2492", "3039", "3695", "4492", "5426", "6555", "7889", "9482", "11360", "13602", "16231", "19348", "23005", "27313", "32364", "38303", "45227", "53341", "62800", "73829" ]
[ "nonn" ]
7
1
2
[ "A000009", "A000041", "A008284", "A008289", "A027193", "A237984", "A240219", "A325347", "A356862", "A359889", "A359893", "A359894", "A359895", "A359897", "A359899", "A359901", "A362562", "A362608", "A363719", "A363720", "A363723", "A363724", "A363725", "A363726", "A363727", "A363731", "A363740" ]
null
Gus Wiseman, Jun 26 2023
2023-06-27T10:28:55
oeisdata/seq/A363/A363740.seq
cbb6e6b722321b0a2df947ade065a6da
A363741
Number of factorizations of n satisfying (mean) = (median) = (mode), assuming there is a unique mode.
[ "0", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
14
1
4
[ "A000041", "A001055", "A008284", "A045778", "A074206", "A089723", "A237984", "A240219", "A316439", "A326567", "A326568", "A326622", "A327472", "A328966", "A339846", "A339890", "A359889", "A359893", "A359909", "A359910", "A359911", "A363719", "A363720", "A363723", "A363727", "A363740", "A363741", "A363742" ]
null
Gus Wiseman, Jun 26 2023
2023-08-16T11:05:38
oeisdata/seq/A363/A363741.seq
e59fbcfbe24b079fb6b52d2b3e14b84c
A363742
Number of integer factorizations of n with different mean, median, and mode.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "3", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "4", "0", "0", "0", "0", "0", "1", "0", "2", "0", "0", "0", "4", "0", "0", "0", "1", "0", "3", "0", "0", "0", "0", "0", "7", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "4", "0", "1", "0", "3", "0", "1", "0", "0", "0", "0", "0", "7" ]
[ "nonn" ]
13
1
48
[ "A001055", "A008284", "A045778", "A074206", "A089723", "A237984", "A240219", "A316439", "A326622", "A339846", "A339890", "A359894", "A359909", "A359910", "A359911", "A362608", "A363265", "A363719", "A363720", "A363725", "A363727", "A363730", "A363741", "A363742" ]
null
Gus Wiseman, Jun 27 2023
2025-01-29T17:30:30
oeisdata/seq/A363/A363742.seq
7cff52af5ed373a8b664cf99cc08edf0
A363743
a(n) = floor(sqrt(log_10(n!))).
[ "0", "0", "0", "0", "1", "1", "1", "1", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11" ]
[ "nonn" ]
42
0
9
[ "A000196", "A034886", "A363743" ]
null
Paul F. Marrero Romero, Aug 17 2023
2023-11-22T22:10:59
oeisdata/seq/A363/A363743.seq
af9cd1495cd597786c2e07f779612a2b
A363744
E.g.f. satisfies A(x) = exp(x * (1 + x * A(x))^2).
[ "1", "1", "5", "31", "313", "3981", "63841", "1223419", "27378737", "701091001", "20221662241", "649032795951", "22945630163017", "886151307346501", "37121193546044609", "1676607954371120611", "81222976991097364321", "4201418329450141471473", "231127287514383805458625" ]
[ "nonn" ]
16
0
3
[ "A125500", "A161635", "A363744", "A365030" ]
null
Seiichi Manyama, Aug 17 2023
2023-11-18T05:00:53
oeisdata/seq/A363/A363744.seq
d5cd7cb996ee200fc165646ce936114d
A363745
Number of integer partitions of n whose rounded-down mean is 2.
[ "0", "0", "1", "0", "2", "2", "3", "4", "10", "6", "16", "21", "24", "32", "58", "47", "85", "111", "119", "158", "248", "217", "341", "442", "461", "596", "867", "792", "1151", "1465", "1506", "1916", "2652", "2477", "3423", "4298", "4381", "5488", "7334", "6956", "9280", "11503", "11663", "14429", "18781", "17992", "23383", "28675", "28970", "35449", "45203" ]
[ "nonn" ]
6
0
5
[ "A000041", "A000975", "A002865", "A008284", "A025065", "A026905", "A027336", "A051293", "A058398", "A067538", "A102627", "A237984", "A241131", "A316413", "A327472", "A327482", "A348551", "A349156", "A363723", "A363745", "A363943", "A363944", "A363945", "A363946", "A363949", "A363950", "A363954" ]
null
Gus Wiseman, Jul 05 2023
2023-07-06T08:54:57
oeisdata/seq/A363/A363745.seq
9852b4c76eb34a22bd1b1229bcf4e703
A363746
Initial digit of the decimal expansion of the tetration n^^n (in Don Knuth's up-arrow notation).
[ "1", "1", "4", "7", "2" ]
[ "base", "hard", "more", "nonn" ]
30
0
3
[ "A000030", "A004231", "A241293", "A241299", "A244059", "A362004", "A363746" ]
null
Marco Ripà, Jun 19 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363746.seq
b8a600aeb98436fe4a3c56a62e534ecd
A363747
Decimal expansion of 2*Integral_{x=0..1} 1/sqrt(1-x^16) dx.
[ "2", "1", "6", "8", "2", "0", "4", "8", "3", "8", "1", "7", "8", "4", "1", "1", "9", "9", "3", "0", "0", "1", "7", "2", "3", "9", "0", "8", "9", "4", "8", "9", "3", "3", "2", "7", "8", "6", "5", "8", "6", "5", "8", "8", "6", "7", "3", "4", "2", "2", "9", "5", "9", "0", "1", "9", "5", "6", "2", "4", "2", "4", "0", "1", "2", "2", "8", "0", "9", "2", "9", "8", "8", "1", "2", "8", "9", "4", "9", "2", "4", "5", "0", "4", "9", "5", "5", "1", "2", "8", "0", "3", "3", "9", "4", "4", "9", "0", "3", "9", "4", "9", "8", "3", "2" ]
[ "nonn", "cons" ]
54
1
1
[ "A000796", "A062539", "A262427", "A363747" ]
null
Christian N. Hofmann, Jun 19 2023
2025-03-27T05:44:04
oeisdata/seq/A363/A363747.seq
d33ad058b904d99403aa1a3bcb9b5c2a
A363748
Number of compositions into sums of fourth powers.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "19", "22", "26", "31", "37", "44", "52", "61", "71", "82", "94", "107", "121", "136", "152", "169", "188", "210", "236", "267", "304", "348", "400", "461", "532", "614", "708", "815", "936", "1072", "1224", "1393", "1581", "1791", "2027", "2294", "2598", "2946", "3346", "3807", "4339", "4953", "5661", "6476", "7412", "8484", "9708", "11101", "12682", "14474" ]
[ "nonn" ]
21
0
17
[ "A000583", "A006456", "A023358", "A291149", "A352529", "A363748", "A363749" ]
null
Seiichi Manyama, Jun 19 2023
2023-06-21T08:56:03
oeisdata/seq/A363/A363748.seq
e52230839f5fc239e4f66f7ec781e517
A363749
Number of compositions into sums of fifth powers.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "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", "35", "38", "42", "47", "53", "60", "68", "77", "87", "98", "110", "123", "137", "152", "168", "185" ]
[ "nonn" ]
17
0
33
[ "A000584", "A006456", "A023358", "A291168", "A352530", "A363748", "A363749" ]
null
Seiichi Manyama, Jun 19 2023
2023-06-19T22:35:40
oeisdata/seq/A363/A363749.seq
17149ee3df25fc2b66c224c7c6ea3f98
A363750
Primes p such that p-1 can be written as a product of smaller numbers that are also of the form prime-1.
[ "2", "5", "13", "17", "37", "41", "61", "73", "89", "97", "101", "109", "113", "157", "181", "193", "233", "241", "257", "277", "281", "313", "337", "349", "353", "397", "401", "409", "421", "433", "449", "457", "461", "521", "541", "577", "593", "601", "613", "617", "641", "661", "673", "701", "733", "757", "761", "769", "821", "829", "877", "881", "929", "937" ]
[ "nonn" ]
13
1
1
[ "A002144", "A006093", "A363636", "A363638", "A363750" ]
null
Pontus von Brömssen, Jun 19 2023
2024-10-25T16:30:28
oeisdata/seq/A363/A363750.seq
a4ecbad511e8ab3bdb2f51e1590d1ad4
A363751
Numbers k such that prime(k) mod k is prime.
[ "3", "4", "7", "8", "9", "13", "15", "16", "18", "20", "22", "24", "26", "28", "30", "31", "32", "33", "34", "36", "38", "39", "40", "42", "43", "44", "45", "47", "48", "49", "50", "51", "52", "53", "55", "57", "59", "60", "65", "66", "69", "72", "73", "74", "76", "78", "82", "84", "86", "88", "90", "92", "96", "98", "100", "102", "106", "108", "112", "116", "120", "126", "128", "130" ]
[ "nonn" ]
27
1
1
[ "A000720", "A004648", "A363751", "A363752" ]
null
Nicholas Leonard, Jun 19 2023
2024-09-06T11:48:01
oeisdata/seq/A363/A363751.seq
207c923a5023ce104f2d62e0cbab971f
A363752
Primes prime(k) such that prime(k) mod k is prime.
[ "5", "7", "17", "19", "23", "41", "47", "53", "61", "71", "79", "89", "101", "107", "113", "127", "131", "137", "139", "151", "163", "167", "173", "181", "191", "193", "197", "211", "223", "227", "229", "233", "239", "241", "257", "269", "277", "281", "313", "317", "347", "359", "367", "373", "383", "397", "421", "433", "443", "457", "463", "479", "503", "521", "541" ]
[ "nonn" ]
28
1
1
[ "A000040", "A004648", "A363751", "A363752" ]
null
Nicholas Leonard, Jun 19 2023
2024-09-06T11:47:45
oeisdata/seq/A363/A363752.seq
4232b564f7d5e9952a84d85e43546d8c
A363753
a(n) = Sum_{k=0..n} (-1)^k*F(k-1)*F(k)*F(k+1)/2, where F(n) is the Fibonacci number A000045(n).
[ "0", "0", "1", "-2", "13", "-47", "213", "-879", "3762", "-15873", "67342", "-285098", "1207966", "-5116586", "21674919", "-91815276", "388937619", "-1647563169", "6979194475", "-29564334305", "125236542640", "-530510487155", "2247278519916", "-9519624520452", "40325776676748", "-170822731106052", "723616701297373" ]
[ "sign", "easy" ]
60
0
4
[ "A000045", "A001655", "A005968", "A119284", "A163198", "A163200", "A215037", "A256178", "A363753", "A363754" ]
null
Hans J. H. Tuenter, Jun 19 2023
2023-08-01T22:01:25
oeisdata/seq/A363/A363753.seq
5fe33c2904ee6d45e4689efc28b12ba9
A363754
a(n) = Sum_{k=0..n} F(2k-1)*F(2k)*F(2k+1)/2, where F(n) is the Fibonacci number A000045(n).
[ "0", "1", "16", "276", "4917", "88132", "1581196", "28372701", "509125596", "9135883240", "163936760185", "2941725767256", "52787126964456", "947226559367881", "16997290941068152", "305004010378316172", "5473074895864584141", "98210344115173624636", "1762313119177232976916", "31623425801074947486405" ]
[ "nonn", "easy" ]
33
0
3
[ "A000045", "A256178", "A363753", "A363754" ]
null
Hans J. H. Tuenter, Jun 19 2023
2023-06-25T03:51:23
oeisdata/seq/A363/A363754.seq
ae4b529182a0ac19179bc2e70b673f41
A363755
The original n X n X n dots problem: minimal number of straight lines (connected at their endpoints) required to join all the n^3 points belonging to the set {{0,1,...,n-1} X {0,1,...,n-1} X {0,1,...,n-1}} in R^3, without any additional constraint.
[ "1", "6", "13" ]
[ "nonn", "more", "hard", "bref" ]
26
1
2
[ "A058992", "A225227", "A261547", "A318165", "A363755" ]
null
Marco Ripà, Jun 19 2023
2025-04-13T07:12:06
oeisdata/seq/A363/A363755.seq
6196e80d3d462d1b4330f5cdad0b3419
A363756
Total number of distinct ways the divisors of n can be the product of other nontrivial divisors of n.
[ "0", "0", "0", "1", "0", "1", "0", "3", "1", "1", "0", "5", "0", "1", "1", "7", "0", "5", "0", "5", "1", "1", "0", "13", "1", "1", "3", "5", "0", "7", "0", "13", "1", "1", "1", "17", "0", "1", "1", "13", "0", "7", "0", "5", "5", "1", "0", "28", "1", "5", "1", "5", "0", "13", "1", "13", "1", "1", "0", "24", "0", "1", "5", "23", "1", "7", "0", "5", "1", "7", "0", "40", "0", "1", "5", "5", "1", "7", "0", "28", "7", "1", "0", "24", "1", "1", "1" ]
[ "nonn", "easy", "changed" ]
9
1
8
[ "A000005", "A001055", "A057567", "A363756" ]
null
Wesley Ivan Hurt, Jun 20 2023
2025-07-07T19:41:31
oeisdata/seq/A363/A363756.seq
89caf219762f93ed4d5c5dc8d3d22dc9
A363757
Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) distinct terms, with pairs numbered according to the position of the second term in the pair.
[ "1", "2", "1", "3", "2", "3", "4", "1", "3", "2", "5", "4", "5", "3", "4", "6", "1", "5", "2", "6", "4", "7", "3", "7", "5", "3", "1", "4", "8", "2", "1", "6", "3", "2", "3", "8", "9", "7", "8", "7", "1", "9", "7", "8", "5", "10", "4", "3", "2", "9", "2", "6", "8", "7", "3", "11", "1", "8", "3", "1", "10", "3", "6", "9", "7", "3", "12", "5", "12", "8", "3", "8", "2", "12", "9", "1", "7", "12", "13", "4", "9", "11", "8", "4", "2", "8", "10", "1", "10", "13", "6" ]
[ "nonn" ]
78
1
2
[ "A026272", "A330896", "A363654", "A363708", "A363757" ]
null
Neal Gersh Tolunsky, Jun 23 2023
2023-07-21T09:15:42
oeisdata/seq/A363/A363757.seq
5c0e20252475faa730d7a1b65ee489cb
A363758
Maximum sum of digits for any number with n digits in fractional base 4/3.
[ "0", "3", "6", "8", "9", "12", "13", "15", "17", "19", "22", "24", "26", "28", "30", "32", "33", "36", "37", "40", "42", "44", "46", "48", "50", "52", "54", "56", "57", "60", "62", "65", "67", "70", "71", "73", "75", "77", "80", "83", "84", "87", "90", "93", "94", "96", "98", "101", "104", "106", "108", "109", "112", "115", "117", "120", "122", "123", "126", "129", "131", "133", "134" ]
[ "nonn", "base" ]
25
0
2
[ "A024631", "A087192", "A244041", "A357425", "A363758" ]
null
Kevin Ryde, Jun 20 2023
2024-03-26T11:16:18
oeisdata/seq/A363/A363758.seq
1f6a6c0a7b450bdc5f86d32f4d7793db
A363759
Smallest number that can be written as a sum of a positive n-th power and a positive (n+1)-th power in 2 different ways.
[ "5", "17", "4097", "1048577", "1073741825", "4398046511105", "72057594037927937", "4722366482869645213697", "1237940039285380274899124225", "1298074214633706907132624082305025", "5444517870735015415413993718908291383297" ]
[ "nonn" ]
21
1
1
[ "A000051", "A016078", "A363759" ]
null
Seiichi Manyama, Jun 20 2023
2023-06-20T15:01:08
oeisdata/seq/A363/A363759.seq
0281d09ed2a40ef63a7a613ffa535df5
A363760
Cycle lengths obtained by repeated application of Klaus Nagel's strip bijection, as described in A307110.
[ "1", "8", "9", "10", "40", "72", "106", "218", "256", "408", "424", "872", "1178", "2336", "2522", "2952", "4712", "10088", "13290", "26648", "28906", "33784", "53160", "115624", "150842", "303784", "330138", "385624", "603368", "1320552", "1716170", "3462216", "3765322", "4397144", "6864680", "15061288", "19543834", "39454792", "42921274", "50118936", "78175336", "171685096" ]
[ "nonn" ]
39
1
2
[ "A362955", "A362956", "A363760", "A367146", "A367148", "A367893" ]
null
Hugo Pfoertner, Jun 26 2023
2023-12-14T08:56:43
oeisdata/seq/A363/A363760.seq
22912136b81c2ed58d998ccc7c2b78a3
A363761
a(n) is the least k < 3*n such that there are exactly n distinct numbers j that can be expressed as sum of two squares with k^2 < j < (k+1)^2, or -1 if such a k does not exist.
[ "0", "1", "2", "4", "5", "7", "8", "10", "13", "12", "15", "17", "19", "23", "21", "24", "25", "28", "32", "31", "34", "37", "39", "44", "41", "43", "45", "50", "51", "48", "57", "55", "56", "59", "64", "63", "68", "69", "74", "77", "78", "75", "72", "80", "88", "84", "-1", "94", "89", "96", "93", "99", "97", "102", "108", "-1", "106", "111", "110", "113", "117", "120", "-1", "123", "133", "127", "130", "137", "142", "138", "139", "-1", "135" ]
[ "sign" ]
19
0
3
[ "A001481", "A004018", "A077773", "A363761", "A363762", "A363763" ]
null
Hugo Pfoertner, Jun 22 2023
2023-07-03T08:01:58
oeisdata/seq/A363/A363761.seq
710358443d4ffb83266df6a939649049
A363762
Numbers k for which A363763(k) = -1.
[ "46", "55", "62", "71", "80", "86", "107", "130", "172", "187", "195", "208", "222", "247", "259", "263", "268", "272", "280", "297", "314", "330", "358", "363", "370", "372", "379", "394", "400", "405", "429", "449", "450", "462", "489", "500", "529", "534", "587", "629", "641", "646", "652", "667", "668", "672", "704", "715", "733", "736", "749", "769", "775", "776", "778", "785", "793", "799" ]
[ "nonn" ]
26
1
1
[ "A001481", "A004018", "A077773", "A363522", "A363761", "A363762" ]
null
Hugo Pfoertner, Jun 20 2023
2023-07-13T07:26:50
oeisdata/seq/A363/A363762.seq
663b59a4af6bf4f840ad6cad6671561f
A363763
a(n) is the least k such that there are exactly n distinct numbers j that can be expressed as the sum of two squares with k^2 < j < (k+1)^2, or -1 if such a k does not exist.
[ "0", "1", "2", "4", "5", "7", "8", "10", "13", "12", "15", "17", "19", "23", "21", "24", "25", "28", "32", "31", "34", "37", "39", "44", "41", "43", "45", "50", "51", "48", "57", "55", "56", "59", "64", "63", "68", "69", "74", "77", "78", "75", "72", "80", "88", "84", "-1", "94", "89", "96", "93", "99", "97", "102", "108", "-1", "106", "111", "110", "113", "117", "120", "-1", "123", "133", "127", "130", "137", "142", "138", "139", "-1", "135" ]
[ "sign" ]
73
0
3
[ "A000415", "A001481", "A004018", "A077773", "A363761", "A363762", "A363763", "A364341" ]
null
Hugo Pfoertner, Jun 20 2023
2023-08-06T04:08:11
oeisdata/seq/A363/A363763.seq
1f78202755bc1827b2fe3b6dd9b36727
A363764
a(1)=1, and thereafter, a(n) is the number of terms in the sequence thus far that appear with a frequency not equal to that of a(n-1).
[ "1", "0", "0", "1", "0", "2", "5", "5", "4", "7", "7", "5", "6", "10", "10", "9", "12", "12", "10", "10", "16", "16", "14", "18", "18", "15", "20", "20", "16", "20", "18", "16", "24", "26", "26", "27", "28", "28", "28", "24", "30", "33", "33", "31", "35", "35", "32", "37", "37", "33", "32", "35", "31", "37", "30", "39", "48", "48", "40", "50", "50", "41", "52", "52", "42", "54", "54", "43", "56", "56", "44", "58", "58" ]
[ "nonn" ]
57
1
6
[ "A350768", "A363301", "A363764" ]
null
Neal Gersh Tolunsky, Jun 28 2023
2023-07-25T09:14:59
oeisdata/seq/A363/A363764.seq
ca74c4ac4e5ab54a849f9fc98c46c867
A363765
Lexicographically earliest sequence of numbers in a hexagonal spiral such that their neighbors have no common digit.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "44", "11", "20", "13", "22", "14", "23", "15", "24", "16", "25", "17", "26", "33", "27", "30", "28", "34", "55", "29", "40", "35", "60", "57", "46", "37", "18", "39", "47", "19", "36", "45", "70", "12", "48", "51", "49", "31", "50", "21", "38", "41", "53", "61", "42", "58", "32", "80", "52", "64", "59", "62", "81", "56", "43", "72" ]
[ "base", "nonn", "fini", "full" ]
41
1
3
[ "A000384", "A003458", "A014105", "A056105", "A363765" ]
null
Carole Dubois, Jun 20 2023
2024-05-31T22:06:46
oeisdata/seq/A363/A363765.seq
58211c127e14ac390f26db97f8e163fa
A363766
Decimal expansion of h-bar*c/eV according to the 2019 SI system in units m.
[ "1", "9", "7", "3", "2", "6", "9", "8", "0", "4", "5", "9", "3", "0", "2", "4", "6", "5", "8", "9", "0", "8", "9", "4", "4", "0", "8", "1", "8", "6", "7", "2", "1", "1", "0", "3", "7", "2", "7", "2", "7", "2", "7", "0", "3", "5", "5", "6", "3", "1", "6", "4", "0", "0", "5", "9", "6", "2", "6", "7", "4", "3", "3", "9", "8", "0", "4", "3", "8", "2", "8", "4", "9", "5", "5", "1", "7", "8", "6", "2", "2", "0", "4", "3", "8", "9", "7" ]
[ "cons", "nonn", "easy" ]
8
-6
2
[ "A003676", "A003678", "A081823", "A254181", "A360750", "A361918", "A362529", "A363766" ]
null
Marco Ripà, Jun 20 2023
2023-08-05T23:39:45
oeisdata/seq/A363/A363766.seq
e49d7ac0a7a37bab037a24b514b8e1ee
A363767
Decimal expansion of 2^(e-2)*e^Sum_{k=2..oo} log(k)/k!.
[ "3", "0", "0", "9", "1", "5", "0", "7", "2", "2", "7", "4", "1", "4", "8", "7", "9", "9", "3", "5", "6", "3", "0", "7", "4", "7", "3", "7", "4", "8", "5", "3", "1", "6", "8", "0", "0", "5", "1", "0", "7", "2", "9", "1", "6", "2", "2", "5", "5", "3", "8", "4", "3", "5", "8", "0", "6", "7", "6", "6", "7", "3", "3", "6", "5", "0", "3", "3", "3", "8", "1", "3", "5", "1", "7", "4", "9", "5", "0", "8", "4", "8", "9", "9", "4", "6", "6", "0", "4", "7", "7", "4", "3", "0", "5", "7", "8", "3", "7", "7" ]
[ "nonn", "cons" ]
20
1
1
[ "A181044", "A296301", "A306243", "A363767" ]
null
Stefano Spezia, Jun 21 2023
2023-06-25T04:24:42
oeisdata/seq/A363/A363767.seq
6cb056b1e6dc579cc6b2d314c09267b2
A363768
The values k such that a regular k-gon with all diagonals drawn contains more 3-sided cells than 4-sided cells.
[ "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "16", "17", "18", "19", "20", "22", "23", "24", "25", "26", "27", "28", "30", "32", "33", "34", "36", "38", "40", "41", "42", "43", "44", "45", "46", "48", "54", "58", "60", "62", "63", "64", "65", "66", "68", "69", "70", "71", "72", "74", "76", "78", "80", "82", "84", "86", "88", "94", "96", "98", "102", "108", "114", "118", "120", "126", "128", "138", "144" ]
[ "nonn" ]
7
1
1
[ "A007678", "A331450", "A349549", "A363768" ]
null
Scott R. Shannon, Jun 21 2023
2023-06-25T08:11:04
oeisdata/seq/A363/A363768.seq
2aa703b211bd7d0383e757b55a8c7a85
A363769
Integers k such that the number of binary partitions of 2k is not a sum of three squares.
[ "10", "18", "34", "40", "58", "66", "72", "90", "106", "114", "130", "136", "154", "160", "170", "178", "202", "210", "226", "232", "250", "258", "264", "282", "288", "298", "306", "330", "338", "354", "360", "378", "394", "402", "418", "424", "442", "450", "456", "474", "490", "498", "514", "520", "538", "544", "554", "562", "586", "594", "610", "616", "634", "640", "650", "658", "674", "680", "698" ]
[ "nonn", "easy" ]
38
1
1
[ "A010060", "A018819", "A353219", "A363769" ]
null
Maciej Ulas, Jun 21 2023
2025-04-13T07:11:41
oeisdata/seq/A363/A363769.seq
b653c4fbe3a760d372b1f2fd83e09e89
A363770
Integers k such that the number of binary partitions of k is not a sum of three squares.
[ "20", "21", "36", "37", "68", "69", "80", "81", "116", "117", "132", "133", "144", "145", "180", "181", "212", "213", "228", "229", "260", "261", "272", "273", "308", "309", "320", "321", "340", "341", "356", "357", "404", "405", "420", "421", "452", "453", "464", "465", "500", "501", "516", "517", "528", "529", "564", "565", "576", "577", "596", "597", "612", "613", "660", "661", "676", "677" ]
[ "nonn", "easy" ]
30
1
1
[ "A004215", "A018819", "A363769", "A363770" ]
null
Maciej Ulas, Jun 21 2023
2023-08-02T12:05:38
oeisdata/seq/A363/A363770.seq
ea8dfbbd070cd3148a933c91b2bdc59c
A363771
Number of graphs (with n vertices) admitting a strictly matched involution.
[ "1", "1", "1", "2", "4", "9", "21", "65", "240", "1128", "6764", "53971" ]
[ "nonn", "hard", "more" ]
14
0
4
[ "A363771", "A363772" ]
null
Stephan Dominique Andres, Jun 21 2023
2023-07-29T21:41:07
oeisdata/seq/A363/A363771.seq
68a77565d5ea789830a72f362b30b114
A363772
Number of graphs (with n edges) admitting a strictly matched involution.
[ "2", "2", "2", "3", "6", "6", "10", "16", "21", "36" ]
[ "nonn", "hard", "more" ]
13
0
1
[ "A363771", "A363772" ]
null
Stephan Dominique Andres, Jun 21 2023
2023-07-30T05:37:11
oeisdata/seq/A363/A363772.seq
9d9665f665778665ab21901e4e8719b8
A363773
a(n) = (4^(n+1) + (-1)^n + 5)/10.
[ "1", "2", "7", "26", "103", "410", "1639", "6554", "26215", "104858", "419431", "1677722", "6710887", "26843546", "107374183", "429496730", "1717986919", "6871947674", "27487790695", "109951162778", "439804651111", "1759218604442", "7036874417767", "28147497671066", "112589990684263", "450359962737050" ]
[ "nonn", "easy" ]
68
0
2
[ "A015521", "A037481", "A363773" ]
null
Evangelos G. Filothodoros, Jun 21 2023
2023-06-29T10:08:54
oeisdata/seq/A363/A363773.seq
39de99fdc51eba13c02810d4d34dabb5
A363774
Expansion of 1/(Sum_{k>=0} x^(k^2))^2.
[ "1", "-2", "3", "-4", "3", "0", "-5", "12", "-18", "18", "-9", "-12", "44", "-76", "93", "-76", "5", "120", "-273", "400", "-414", "228", "200", "-828", "1480", "-1842", "1539", "-268", "-2004", "4824", "-7168", "7568", "-4518", "-2784", "13577", "-24900", "31563", "-27236", "6816", "30308", "-77010", "116844", "-126018", "80180", "34140", "-205932", "389275" ]
[ "sign", "easy" ]
15
0
2
[ "A000925", "A162552", "A274621", "A363774", "A363778" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:22
oeisdata/seq/A363/A363774.seq
5066397e879e3be1b8d8db8ca3d44c4b
A363775
Expansion of 1/(Sum_{k>=0} x^(k^2))^3.
[ "1", "-3", "6", "-10", "12", "-9", "-2", "24", "-54", "80", "-84", "42", "66", "-234", "420", "-536", "450", "-39", "-740", "1770", "-2688", "2898", "-1722", "-1320", "6078", "-11349", "14736", "-12992", "3084", "15999", "-41212", "64032", "-70788", "46020", "20778", "-126132", "244120", "-323421", "295410", "-96848", "-293868", "815829", "-1297972" ]
[ "sign", "easy" ]
14
0
2
[ "A002102", "A162552", "A363775", "A363778" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:26
oeisdata/seq/A363/A363775.seq
3aad4dbe6af2919c20edee7ddf35873a
A363776
Expansion of 1/(Sum_{k>=0} x^(k^3))^2.
[ "1", "-2", "3", "-4", "5", "-6", "7", "-8", "7", "-4", "-1", "8", "-17", "28", "-41", "56", "-70", "80", "-83", "76", "-56", "20", "35", "-112", "210", "-324", "445", "-562", "658", "-712", "699", "-590", "357", "22", "-558", "1252", "-2084", "3008", "-3947", "4788", "-5383", "5556", "-5116", "3864", "-1618", "-1756", "6307", "-11956", "18454", "-25348", "31962", "-37380" ]
[ "sign", "easy" ]
13
0
2
[ "A173677", "A363776", "A363779", "A363783" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:44
oeisdata/seq/A363/A363776.seq
03aead1cffcc63c503121ece222ce46e
A363777
Expansion of 1/(Sum_{k>=0} x^(k^3))^3.
[ "1", "-3", "6", "-10", "15", "-21", "28", "-36", "42", "-43", "36", "-18", "-14", "63", "-132", "224", "-336", "459", "-578", "672", "-714", "671", "-504", "168", "378", "-1161", "2184", "-3419", "4794", "-6183", "7396", "-8169", "8169", "-7014", "4308", "321", "-7156", "16311", "-27636", "40607", "-54222", "66924", "-76572", "80451", "-75372", "57883" ]
[ "sign", "easy" ]
14
0
2
[ "A051343", "A363777", "A363779", "A363783" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:49
oeisdata/seq/A363/A363777.seq
2f3b383db8c7840a06909ecfda918dd7
A363778
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^2))^k.
[ "1", "1", "0", "1", "-1", "0", "1", "-2", "1", "0", "1", "-3", "3", "-1", "0", "1", "-4", "6", "-4", "0", "0", "1", "-5", "10", "-10", "3", "1", "0", "1", "-6", "15", "-20", "12", "0", "-2", "0", "1", "-7", "21", "-35", "31", "-9", "-5", "3", "0", "1", "-8", "28", "-56", "65", "-36", "-2", "12", "-3", "0", "1", "-9", "36", "-84", "120", "-96", "24", "24", "-18", "1", "0", "1", "-10", "45", "-120", "203", "-210", "105", "20", "-54", "18", "2", "0" ]
[ "sign", "tabl" ]
13
0
8
[ "A000007", "A045847", "A162552", "A317665", "A363774", "A363775", "A363778", "A363779", "A363780" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:21:03
oeisdata/seq/A363/A363778.seq
42c5fe0e4b7c1cb7c786fc2addc22849
A363779
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^3))^k.
[ "1", "1", "0", "1", "-1", "0", "1", "-2", "1", "0", "1", "-3", "3", "-1", "0", "1", "-4", "6", "-4", "1", "0", "1", "-5", "10", "-10", "5", "-1", "0", "1", "-6", "15", "-20", "15", "-6", "1", "0", "1", "-7", "21", "-35", "35", "-21", "7", "-1", "0", "1", "-8", "28", "-56", "70", "-56", "28", "-8", "0", "0", "1", "-9", "36", "-84", "126", "-126", "84", "-36", "7", "1", "0", "1", "-10", "45", "-120", "210", "-252", "210", "-120", "42", "-4", "-2", "0" ]
[ "sign", "tabl" ]
16
0
8
[ "A000007", "A290054", "A323633", "A363776", "A363777", "A363778", "A363779", "A363781", "A363783" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:55
oeisdata/seq/A363/A363779.seq
644a7fef2c94b43a2a59106f3a61ac4c
A363780
a(n) = [x^n] 1/(Sum_{k>=0} x^(k^2))^n.
[ "1", "-1", "3", "-10", "31", "-96", "294", "-876", "2511", "-6796", "16698", "-33540", "31174", "184534", "-1627812", "8912760", "-41466433", "176963760", "-714194382", "2766892840", "-10374065814", "37815483948", "-134334781732", "465432203640", "-1571910265770", "5164302815179", "-16438631981418" ]
[ "sign" ]
11
0
3
[ "A287617", "A363778", "A363780" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:22:01
oeisdata/seq/A363/A363780.seq
8a45823310cb9d8824b2b2a759890852
A363781
a(n) = [x^n] 1/(Sum_{k>=0} x^(k^3))^n.
[ "1", "-1", "3", "-10", "35", "-126", "462", "-1716", "6427", "-24220", "91718", "-348712", "1330238", "-5088916", "19515660", "-75000600", "288772795", "-1113688667", "4301387580", "-16635049690", "64410064110", "-249659926890", "968651123520", "-3761601535620", "14619516646150", "-56861702382576" ]
[ "sign" ]
10
0
3
[ "A291700", "A363779", "A363781" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T07:20:59
oeisdata/seq/A363/A363781.seq
74415d9227e24f361e0d2b5f65a11ad0
A363782
Products of three distinct strong primes.
[ "5423", "6919", "7667", "11033", "11803", "12529", "13079", "13277", "14773", "16687", "18139", "18241", "18821", "18887", "20009", "20213", "21373", "22649", "23749", "24013", "25201", "25619", "25789", "26609", "27269", "27863", "28897", "29087", "30217", "30481", "30943", "32021", "32153", "32219", "33031", "33473", "34133", "35003", "35629", "35717", "36839" ]
[ "nonn" ]
22
1
1
[ "A007304", "A051634", "A363167", "A363782", "A364738" ]
null
Massimo Kofler, Jun 21 2023
2024-08-21T19:34:48
oeisdata/seq/A363/A363782.seq
63a6bcf32828d405054e759b9f597d80
A363783
L.g.f.: log( Sum_{k>=0} x^(k^3) ).
[ "1", "-1", "1", "-1", "1", "-1", "1", "7", "-8", "9", "-10", "11", "-12", "13", "-14", "7", "1", "-10", "20", "-31", "43", "-56", "70", "-77", "76", "-66", "73", "-43", "1", "54", "-123", "199", "-274", "339", "-419", "470", "-480", "436", "-324", "137", "124", "-449", "861", "-1332", "1822", "-2278", "2633", "-2813", "2745", "-2366", "1582", "-326", "-1430", "3635", "-6225", "9037", "-11836", "14325", "-16106", "16706", "-15615" ]
[ "sign" ]
13
1
8
[ "A162552", "A363783", "A363784" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T10:40:15
oeisdata/seq/A363/A363783.seq
c7a94802440229edcc9a19f2c3fe1986
A363784
L.g.f.: log( Sum_{k>=0} x^(k^4) ).
[ "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "15", "-16", "17", "-18", "19", "-20", "21", "-22", "23", "-24", "25", "-26", "27", "-28", "29", "-30", "15", "1", "-18", "36", "-55", "75", "-96", "118", "-141", "165", "-190", "216", "-243", "271", "-300", "330", "-345", "344", "-326", "290", "-235", "160", "-64", "-54", "195", "-360", "550", "-766", "1009", "-1280", "1580" ]
[ "sign" ]
10
1
16
[ "A162552", "A363783", "A363784" ]
null
Seiichi Manyama, Jun 21 2023
2023-06-22T10:40:20
oeisdata/seq/A363/A363784.seq
44de844b20facf36df0e3c14f8b1d0c1
A363785
A variant of payphone permutations: given a row of n payphones, a(n) is the number ways for n people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones.
[ "1", "2", "4", "6", "16", "28", "120", "264", "576", "2784", "11040", "37440", "204672", "679680", "2511360", "15655680", "52945920", "232796160", "2456801280", "11867627520", "97875025920", "576737280000", "4012233523200", "20013325516800", "215802239385600", "1778700504268800", "9687506721177600", "88613303353344000", "448250987623219200" ]
[ "nonn" ]
8
1
2
[ "A095236", "A095239", "A095912", "A358056", "A361294", "A361295", "A361296", "A362192", "A363785" ]
null
Max Alekseyev, Jun 21 2023
2023-06-22T06:05:40
oeisdata/seq/A363/A363785.seq
faa7ce3ec744fb35e9b08170a86afa7d
A363786
a(0) = 2. For n >= 1, a(n) is the least prime p such that a(n-1) + p has n prime factors counted with multiplicity.
[ "2", "3", "3", "5", "11", "37", "59", "229", "347", "421", "3163", "4517", "1627", "26021", "14939", "34213", "64091", "378277", "14939", "3392933", "146011", "6931877", "8796763", "37340581", "25573979", "238667173", "113654363", "1018807717", "491141723", "4743349669", "8544205403", "10246276517", "491141723" ]
[ "nonn" ]
8
0
1
[ "A001222", "A357713", "A363786" ]
null
Zak Seidov and Robert Israel, Jun 21 2023
2023-06-22T06:03:59
oeisdata/seq/A363/A363786.seq
b2496ed42d292d77e3287b5257c97ed7
A363787
Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.
[ "1", "6", "10", "18", "21", "34", "55", "60", "66", "69", "81", "92", "108", "115", "116", "126", "130", "155", "156", "172", "180", "185", "204", "205", "212", "222", "228", "246", "258", "261", "273", "284", "285", "295", "300", "308", "318", "321", "332", "340", "345", "355", "356", "366", "378", "395", "396", "404", "405", "414", "420", "425", "438", "452", "462" ]
[ "nonn", "easy", "base" ]
10
1
2
[ "A049445", "A144302", "A356349", "A363787", "A363788", "A363789" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:22:08
oeisdata/seq/A363/A363787.seq
ff1f7c969917346fc6c5cc0f8784b836
A363788
Even primitive binary Niven numbers: even terms of A363787.
[ "6", "10", "18", "34", "60", "66", "92", "108", "116", "126", "130", "156", "172", "180", "204", "212", "222", "228", "246", "258", "284", "300", "308", "318", "332", "340", "356", "366", "378", "396", "404", "414", "420", "438", "452", "462", "474", "486", "498", "514", "540", "556", "564", "588", "596", "606", "612", "630", "652", "660", "676", "708", "726", "780" ]
[ "nonn", "easy", "base" ]
6
1
1
[ "A049445", "A052548", "A144302", "A358255", "A363787", "A363788" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:22:24
oeisdata/seq/A363/A363788.seq
34105be663107f0c999090dc17d861d6
A363789
a(n) is the smallest primitive binary Niven number (A363787) whose binary representation is ending with n zeros.
[ "1", "6", "60", "2040", "1048560", "137438953440", "1180591620717411303360", "43556142965880123323311949751266331066240", "29642774844752946028434172162224104410437116074403984394101141506025761187823360" ]
[ "nonn", "easy", "base" ]
6
0
2
[ "A000120", "A007814", "A049445", "A066524", "A143115", "A358256", "A363787", "A363789" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:22:39
oeisdata/seq/A363/A363789.seq
424b7506ff3f3b63ec345f65283d1feb
A363790
Numbers k such that k and k+1 are both primitive binary Niven numbers (A363787).
[ "115", "155", "204", "284", "355", "395", "404", "555", "564", "595", "675", "804", "835", "846", "1075", "1124", "1164", "1182", "1266", "1315", "1434", "1555", "1604", "1686", "1795", "1938", "2075", "2124", "2195", "2244", "2315", "2324", "2358", "2435", "2595", "3084", "3204", "3282", "3366", "4124", "4195", "4206", "4235", "4244", "4364", "4458" ]
[ "nonn", "base" ]
6
1
1
[ "A049445", "A330931", "A363787", "A363790", "A363791", "A363792" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:22:50
oeisdata/seq/A363/A363790.seq
bbb763c4fa497c220ea70e01e3969b80
A363791
Starts of runs of 3 consecutive integers that are primitive binary Niven numbers (A363787).
[ "4184046", "5234670", "6285294", "7861230", "8123886", "8255214", "8255215", "8320878", "8353710", "8370126", "8379247", "12238830", "12451631", "12572622", "13623246", "13629935", "14515182", "14646510", "14673870", "14673871", "14679342", "15040494", "15335375", "15449071", "15531759", "15708078", "15986543", "16178670" ]
[ "nonn", "base" ]
6
1
1
[ "A049445", "A330931", "A330932", "A363787", "A363790", "A363791", "A363792" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:23:02
oeisdata/seq/A363/A363791.seq
d4967e80ce5d7bdd57bcce23e34d9d14
A363792
Starts of runs of 4 consecutive integers that are primitive binary Niven numbers (A363787).
[ "8255214", "14673870", "29092590", "33185646", "41743854", "47697390", "48069486", "56348622", "56999790", "58116078", "59604462", "60534702", "60813774", "61837038", "62581230", "64069614", "64999854", "65371950", "66581262", "66674286", "75232494", "83418606", "86767470", "88069806", "92255886", "95418702", "96441966", "99511758", "99604782" ]
[ "nonn", "base" ]
6
1
1
[ "A049445", "A330931", "A330932", "A330933", "A363787", "A363790", "A363791", "A363792" ]
null
Amiram Eldar, Jun 22 2023
2023-06-24T13:23:11
oeisdata/seq/A363/A363792.seq
5b5ffa6edaaadcebd12e68d354f13e34
A363793
Number of Q-isomorphism classes of elliptic curves E/Q with good reduction away from prime(n).
[ "24", "8", "0", "4", "12", "0", "8", "8", "0", "0", "0", "16", "0", "6", "2", "2", "0", "2", "4", "0", "4", "4", "2", "6", "0", "2", "0", "0", "2", "4", "0", "2", "0", "2", "0", "0", "2", "4", "0", "0", "4", "0", "2", "0", "2", "0", "0", "0", "0", "2", "4", "0", "0", "0", "0", "0", "2", "0", "4", "0", "0", "0", "10", "0", "0", "0", "2", "0", "2", "0", "4", "6", "0", "2", "0", "0", "2", "4", "0", "0", "0", "0", "6", "4", "0", "8", "0", "0", "0", "0", "2", "0", "0", "0", "0", "8" ]
[ "nonn" ]
15
1
1
[ "A000040", "A110620", "A332545", "A359480", "A361661", "A363793" ]
null
Robin Visser, Jun 22 2023
2023-08-20T10:49:50
oeisdata/seq/A363/A363793.seq
0c2cb2d58acfad75408bc9da082d56e2
A363794
a(n) = smallest prime(n)-smooth number k such that r(k) >= r(P(n+1)), where r(n) = A010846(n) and P(n) = A002110(n).
[ "16", "72", "540", "6300", "92400", "1681680", "36756720", "921470550", "27886608750", "970453984500", "37905932634570" ]
[ "nonn", "hard", "more" ]
13
1
1
[ "A000079", "A000961", "A002110", "A002473", "A003586", "A007947", "A010846", "A051037", "A051038", "A080197", "A080681", "A080682", "A080683", "A162306", "A363061", "A363794" ]
null
Michael De Vlieger, Jun 22 2023
2024-07-08T08:51:06
oeisdata/seq/A363/A363794.seq
bb19841790f7bd62b362760178818e66
A363795
Number of divisors of n of the form 7*k + 2.
[ "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "2", "0", "2", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "2", "0", "2", "0", "1", "0", "2", "1", "1", "0", "1", "0", "1", "0", "2", "1", "2", "0", "2", "0", "1", "1", "1", "0", "2", "0", "1", "0", "2", "0", "2", "0", "1", "1", "2", "1", "1", "0", "1", "1", "1", "0", "3", "0", "2", "0", "1", "0", "1", "1", "2", "1", "1", "0", "1", "0", "2", "0", "2", "0", "3", "0", "2", "1", "1", "0", "2", "0", "1", "1" ]
[ "nonn", "easy" ]
32
1
16
[ "A001620", "A001822", "A001877", "A016630", "A279061", "A284443", "A354628", "A363795", "A363805", "A363806", "A363807", "A363808" ]
null
Seiichi Manyama, Jun 23 2023
2023-11-25T04:28:00
oeisdata/seq/A363/A363795.seq
ead705e2024d790d0308061ff9529462
A363796
a(n) is the least prime p such that p^n + 2*n is prime, or -1 if there is no such p.
[ "3", "3", "5", "3", "13", "31", "5", "3", "71", "3", "1279", "-1", "641", "3", "11", "-1", "3", "5", "317", "2477", "191", "-1", "2473", "-1", "59", "31", "5", "-1", "3061", "907", "401", "-1", "353", "3", "1153", "431", "113", "1949", "7", "-1", "7027", "1063", "23", "2239", "1109", "-1", "2887", "41", "251", "953", "2543", "-1", "367", "607", "59", "1627", "43", "-1", "67", "-1", "5", "307", "257", "-1", "1483", "-1", "353" ]
[ "sign" ]
14
1
1
[ "A363796", "A363797", "A363798" ]
null
Robert Israel, Jun 22 2023
2023-07-07T05:47:04
oeisdata/seq/A363/A363796.seq
3016257bc6e49da0b969f18342dca2bd
A363797
Numbers k such that 3^k + 2*k is prime.
[ "1", "2", "4", "8", "10", "14", "17", "34", "74", "127", "137", "160", "925", "1117", "5767", "11810", "15220", "37015", "46289" ]
[ "nonn", "more" ]
26
1
2
[ "A363796", "A363797" ]
null
Robert Israel, Jun 23 2023
2024-10-19T08:33:52
oeisdata/seq/A363/A363797.seq
26c90b0e494eaa127eb20c74181202a5
A363798
Numbers k such that there is no prime p for which p^k + 2*k is prime.
[ "12", "16", "22", "24", "28", "32", "40", "46", "52", "58", "60", "64", "66", "70", "72", "76", "82", "84", "88", "92", "94", "100", "106", "108", "112", "118", "124", "130", "132", "136", "142", "144", "148", "150", "152", "154", "166", "170", "172", "178", "180", "184", "190", "192", "196", "202", "208", "212", "214", "220", "226", "232", "234", "238", "240", "244", "250", "252", "256", "262", "264", "268", "272", "274" ]
[ "nonn" ]
4
1
1
[ "A363796", "A363798" ]
null
Robert Israel, Jun 23 2023
2023-07-07T05:47:16
oeisdata/seq/A363/A363798.seq
9a467cdad8b859c8b89bdf2c0183d26c
A363799
Numbers whose binary representation has more 1-bits than its cube.
[ "407182835067", "445317119867", "478351981947", "814365670134", "873268508637", "890634239734", "956703963894", "956703964539", "1628731340268", "1746537017274", "1781268479468", "1913407927788", "1913407929078", "2774213097787", "3257462680536", "3493074034548", "3562536958936", "3573277243773" ]
[ "nonn", "base" ]
31
1
1
[ "A000120", "A094694", "A138597", "A192085", "A363799" ]
null
Zhao Hui Du, Jun 23 2023
2023-08-07T12:28:30
oeisdata/seq/A363/A363799.seq
2364cfad140f446b6ba45436b2523e69
A363800
Expansion of Product_{k>0} (1 - x^(7*k-5)) * (1 - x^(7*k-2)) * (1 - x^(7*k)).
[ "1", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "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", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "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", "0", "-1", "0", "0", "0" ]
[ "sign" ]
12
0
null
[ "A186029", "A218471", "A232714", "A346797", "A363800", "A363801", "A363803" ]
null
Seiichi Manyama, Jun 23 2023
2023-06-23T10:31:57
oeisdata/seq/A363/A363800.seq
ce01fce0502ae2f2c0833a16edded99b