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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A006501
Expansion of (1+x^2) / ( (1-x)^2 * (1-x^3)^2 ).
[ "1", "2", "4", "8", "12", "18", "27", "36", "48", "64", "80", "100", "125", "150", "180", "216", "252", "294", "343", "392", "448", "512", "576", "648", "729", "810", "900", "1000", "1100", "1210", "1331", "1452", "1584", "1728", "1872", "2028", "2197", "2366", "2548", "2744", "2940", "3150", "3375", "3600", "3840", "4096", "4352", "4624", "4913", "5202" ]
[ "nonn", "easy" ]
71
0
2
[ "A000578", "A002117", "A002620", "A006501", "A008233", "A008382", "A008881", "A009641", "A009694", "A009714", "A144677", "A210433", "A354600" ]
[ "M1091" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006501.seq
257113250cdd398be750f6f50c7883db
A006502
Related to Fibonacci numbers.
[ "1", "3", "14", "60", "279", "1251", "5329", "21532", "83225", "310464", "1126502", "4000602", "13973725", "48187521", "164535708", "557528652", "1878067349", "6297614277", "21043287325", "70125062642", "233198372319", "774246922848", "2567419361916", "8505547438596", "28157369861593", "93162331494255", "308108749498202" ]
[ "nonn" ]
27
0
2
[ "A006502", "A259708" ]
[ "M2970" ]
N. J. A. Sloane.
2025-01-05T19:51:34
oeisdata/seq/A006/A006502.seq
86d16305550e59a5d5b87acd2583931b
A006503
a(n) = n*(n+1)*(n+8)/6.
[ "0", "3", "10", "22", "40", "65", "98", "140", "192", "255", "330", "418", "520", "637", "770", "920", "1088", "1275", "1482", "1710", "1960", "2233", "2530", "2852", "3200", "3575", "3978", "4410", "4872", "5365", "5890", "6448", "7040", "7667", "8330", "9030", "9768", "10545", "11362", "12220", "13120", "14063", "15050", "16082", "17160", "18285" ]
[ "nonn", "easy" ]
67
0
2
[ "A000027", "A000096", "A000292", "A002378", "A006503", "A006504", "A095660", "A144064" ]
[ "M2835" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006503.seq
e900390c57eb37312935940e6aa8fc44
A006504
Coefficient of x^4 in (1-x-x^2)^(-n).
[ "5", "20", "51", "105", "190", "315", "490", "726", "1035", "1430", "1925", "2535", "3276", "4165", "5220", "6460", "7905", "9576", "11495", "13685", "16170", "18975", "22126", "25650", "29575", "33930", "38745", "44051", "49880", "56265", "63240", "70840", "79101", "88060", "97755", "108225", "119510", "131651", "144690", "158670" ]
[ "nonn", "easy" ]
51
1
1
[ "A006504", "A144064" ]
[ "M3895" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006504.seq
edd9a9b728a77082ba8b3193e607c0fc
A006505
Number of partitions of an n-set into boxes of size >2.
[ "1", "0", "0", "1", "1", "1", "11", "36", "92", "491", "2557", "11353", "60105", "362506", "2169246", "13580815", "91927435", "650078097", "4762023647", "36508923530", "292117087090", "2424048335917", "20847410586719", "185754044235873", "1711253808769653", "16272637428430152" ]
[ "nonn", "easy" ]
73
0
7
[ "A000110", "A000296", "A006505", "A057814", "A057837", "A059022", "A293024", "A293038" ]
[ "M4789" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006505.seq
b3ec0689c078c3d51186e70f17c0e66e
A006506
Number of n X n binary matrices with no 2 adjacent 1's, or number of configurations of non-attacking princes on an n X n board, where a "prince" attacks the four adjacent (non-diagonal) squares. Also number of independent vertex sets in an n X n grid.
[ "1", "2", "7", "63", "1234", "55447", "5598861", "1280128950", "660647962955", "770548397261707", "2030049051145980050", "12083401651433651945979", "162481813349792588536582997", "4935961285224791538367780371090", "338752110195939290445247645371206783", "52521741712869136440040654451875316861275" ]
[ "nonn", "nice", "hard" ]
162
0
2
[ "A006506", "A027683", "A089934", "A191779", "A201511", "A212270", "A232833" ]
[ "M1816" ]
N. J. A. Sloane, R. H. Hardin, Paul Zimmermann
2025-02-16T08:32:30
oeisdata/seq/A006/A006506.seq
d7b59ba952901bc18d4cd0642c3dfe09
A006507
a(n+1) = a(n) + sum of digits of a(n), with a(1)=7.
[ "7", "14", "19", "29", "40", "44", "52", "59", "73", "83", "94", "107", "115", "122", "127", "137", "148", "161", "169", "185", "199", "218", "229", "242", "250", "257", "271", "281", "292", "305", "313", "320", "325", "335", "346", "359", "376", "392", "406", "416", "427", "440", "448", "464", "478", "497", "517", "530", "538", "554", "568" ]
[ "base", "nonn" ]
32
1
1
[ "A006507", "A007618", "A016052", "A016096" ]
[ "M4348" ]
N. J. A. Sloane
2023-04-21T11:37:54
oeisdata/seq/A006/A006507.seq
a38e65cd8dfaea906034690971d64fa3
A006508
a(n+1) = a(n)-th composite number, with a(0) = 1.
[ "1", "4", "9", "16", "26", "39", "56", "78", "106", "141", "184", "236", "299", "374", "465", "570", "696", "843", "1014", "1212", "1441", "1708", "2014", "2365", "2769", "3226", "3749", "4343", "5016", "5774", "6630", "7596", "8676", "9897", "11259", "12784", "14482", "16383", "18502", "20847", "23458", "26354", "29562", "33112", "37041", "41370" ]
[ "nonn", "easy" ]
42
0
2
[ "A002808", "A006508", "A007097" ]
[ "M3357" ]
N. J. A. Sloane
2018-05-02T14:42:10
oeisdata/seq/A006/A006508.seq
d285ddeeee638a8ba2bb9d802984fec0
A006509
Cald's sequence: a(n+1) = a(n) - prime(n) if that value is positive and new, otherwise a(n) + prime(n) if new, otherwise 0; start with a(1)=1.
[ "1", "3", "6", "11", "4", "15", "2", "19", "38", "61", "32", "63", "26", "67", "24", "71", "18", "77", "16", "83", "12", "85", "164", "81", "170", "73", "174", "277", "384", "275", "162", "35", "166", "29", "168", "317", "468", "311", "148", "315", "142", "321", "140", "331", "138", "335", "136", "347", "124", "351", "122", "355", "116", "357", "106", "363", "100", "369", "98", "375", "94", "377", "84", "391", "80", "393", "76", "407", "70", "417", "68", "421", "62", "429", "56", "435", "52", "441", "44", "445", "36", "455", "34", "465", "898", "459", "902", "453", "910", "449", "912", "1379", "900", "413", "904", "405", "908", "399", "920", "397", "938", "1485", "928", "365", "934", "1505", "2082", "1495", "2088", "1489", "888", "281", "894", "1511", "892", "261", "0", "643", "1290", "637", "1296", "635", "1308", "631", "1314", "623", "1324", "615", "1334", "607", "1340" ]
[ "nonn", "nice" ]
83
1
2
[ "A000040", "A005132", "A006509", "A064365", "A093903", "A111338", "A111339", "A112877", "A117128", "A117129", "A370951" ]
[ "M2539" ]
N. J. A. Sloane
2024-03-07T15:02:25
oeisdata/seq/A006/A006509.seq
d1755c2f6b7f29da11d852062792ebfb
A006510
Duplicate of A006055.
[ "2", "3", "5", "7", "23", "67", "89", "4567", "78901", "678901", "23456789", "45678901", "9012345678901" ]
[ "dead" ]
12
1
1
null
[ "M5135" ]
N. J. A. Sloane, Jun 13 2012
2012-06-13T12:35:24
oeisdata/seq/A006/A006510.seq
62e17661cb36f9ea865b8541b98e2f35
A006511
Largest inverse of totient function (A000010): a(n) is the largest x such that phi(x) = m, where m = A002202(n) is the n-th number in the range of phi.
[ "2", "6", "12", "18", "30", "22", "42", "60", "54", "66", "46", "90", "58", "62", "120", "126", "150", "98", "138", "94", "210", "106", "162", "174", "118", "198", "240", "134", "142", "270", "158", "330", "166", "294", "276", "282", "420", "250", "206", "318", "214", "378", "242", "348", "354", "462", "254", "510", "262", "414", "274", "278", "426", "630", "298", "302" ]
[ "nonn" ]
37
1
1
[ "A000010", "A002181", "A002202", "A006511", "A036912", "A036913", "A057826", "A132154" ]
[ "M1580" ]
N. J. A. Sloane
2024-11-14T06:00:12
oeisdata/seq/A006/A006511.seq
4dcfac8962f8504edacb46fb18ec693e
A006512
Greater of twin primes.
[ "5", "7", "13", "19", "31", "43", "61", "73", "103", "109", "139", "151", "181", "193", "199", "229", "241", "271", "283", "313", "349", "421", "433", "463", "523", "571", "601", "619", "643", "661", "811", "823", "829", "859", "883", "1021", "1033", "1051", "1063", "1093", "1153", "1231", "1279", "1291", "1303", "1321", "1429", "1453", "1483", "1489", "1609" ]
[ "nonn", "nice", "easy" ]
165
1
1
[ "A001097", "A001359", "A002476", "A006512", "A014574", "A067829", "A077800", "A139690" ]
[ "M3763" ]
N. J. A. Sloane
2025-02-08T11:08:54
oeisdata/seq/A006/A006512.seq
5c4fd5f2f88f24619f11c9c002baebb2
A006513
Limit of the image of n after 2k iterates of `(3x+1)/2' map as k grows.
[ "1", "2", "2", "1", "1", "1", "2", "2", "2", "2", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "2", "2", "2", "2", "2", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
20
1
2
[ "A006513", "A014682" ]
[ "M0189" ]
N. J. A. Sloane.
2022-02-03T11:17:13
oeisdata/seq/A006/A006513.seq
99cf82805c626c2b3e9f39978d66fdb1
A006514
Primes p such that 2^p - 1 has at most 2 prime factors.
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "31", "37", "41", "59", "61", "67", "83", "89", "97", "101", "103", "107", "109", "127", "131", "137", "139", "149", "167", "197", "199", "227", "241", "269", "271", "281", "293", "347", "373", "379", "421", "457", "487", "521", "523", "607", "727", "809", "881", "971", "983", "997", "1061", "1063" ]
[ "nonn" ]
25
1
1
[ "A000043", "A001348", "A006514", "A088863" ]
[ "M0653" ]
N. J. A. Sloane.
2019-04-23T22:17:29
oeisdata/seq/A006/A006514.seq
7b70b32dabae6a46ef644b4cf3f11315
A006515
Mersenne numbers with at most 2 prime factors.
[ "3", "7", "31", "127", "2047", "8191", "131071", "524287", "8388607", "2147483647", "137438953471", "2199023255551", "576460752303423487", "2305843009213693951", "147573952589676412927", "9671406556917033397649407", "618970019642690137449562111", "158456325028528675187087900671" ]
[ "nonn" ]
27
1
1
[ "A000225", "A001348", "A006514", "A006515" ]
[ "M2695" ]
N. J. A. Sloane.
2023-09-19T01:44:18
oeisdata/seq/A006/A006515.seq
dae129e71055276f6e2a7754473756cf
A006516
a(n) = 2^(n-1)*(2^n - 1), n >= 0.
[ "0", "1", "6", "28", "120", "496", "2016", "8128", "32640", "130816", "523776", "2096128", "8386560", "33550336", "134209536", "536854528", "2147450880", "8589869056", "34359607296", "137438691328", "549755289600", "2199022206976", "8796090925056", "35184367894528", "140737479966720", "562949936644096" ]
[ "nonn", "nice", "easy" ]
260
0
3
[ "A000043", "A000108", "A000384", "A000396", "A002001", "A002450", "A003462", "A005059", "A006095", "A006516", "A007582", "A010036", "A010684", "A016290", "A048473", "A049072", "A065442", "A079598", "A109241", "A134346", "A139251", "A151821", "A153006", "A171476", "A201461", "A211705" ]
[ "M4183" ]
N. J. A. Sloane
2025-03-22T15:21:42
oeisdata/seq/A006/A006516.seq
41fc632716b992ea351f4646699e6f79
A006517
Numbers k such that k divides 2^k + 2.
[ "1", "2", "6", "66", "946", "8646", "180246", "199606", "265826", "383846", "1234806", "3757426", "9880278", "14304466", "23612226", "27052806", "43091686", "63265474", "66154726", "69410706", "81517766", "106047766", "129773526", "130520566", "149497986", "184416166", "279383126" ]
[ "nonn", "nice" ]
56
1
2
[ "A006517", "A006521", "A015888", "A015889", "A015891", "A015892", "A015893", "A015897", "A015898", "A015902", "A015903", "A015904", "A015905", "A015906" ]
[ "M1719" ]
N. J. A. Sloane, David W. Wilson
2024-02-27T01:09:56
oeisdata/seq/A006/A006517.seq
a98504d2e527c2840ecff01a9bc3c977
A006518
Continued fraction for Sum_{k >= 2} 2^(-Fibonacci(k)).
[ "0", "1", "10", "6", "1", "6", "2", "14", "4", "124", "2", "1", "2", "2039", "1", "9", "1", "1", "1", "262111", "2", "8", "1", "1", "1", "3", "1", "536870655", "4", "16", "3", "1", "3", "7", "1", "140737488347135", "8", "128", "2", "1", "1", "1", "7", "2", "1", "9", "1" ]
[ "nonn", "cofr" ]
38
0
3
[ "A000045", "A006518", "A084119", "A124091", "A125600", "A181313" ]
[ "M4677" ]
N. J. A. Sloane
2021-08-23T00:42:36
oeisdata/seq/A006/A006518.seq
8d9345efdf6e12b1bf73ac07974caad3
A006519
Highest power of 2 dividing n.
[ "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "32", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "64", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "32", "1", "2", "1", "4", "1", "2" ]
[ "nonn", "easy", "nice", "mult", "hear" ]
269
1
2
[ "A000079", "A001511", "A001620", "A002487", "A003484", "A004198", "A006519", "A006520", "A007814", "A007913", "A022560", "A038712", "A059897", "A091476", "A100338", "A101119", "A135416", "A135481", "A139250", "A171977", "A225546" ]
[ "M0162" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:30
oeisdata/seq/A006/A006519.seq
fac9cadb4c2ea9614e1bf91f240ece32
A006520
Partial sums of A006519.
[ "1", "3", "4", "8", "9", "11", "12", "20", "21", "23", "24", "28", "29", "31", "32", "48", "49", "51", "52", "56", "57", "59", "60", "68", "69", "71", "72", "76", "77", "79", "80", "112", "113", "115", "116", "120", "121", "123", "124", "132", "133", "135", "136", "140", "141", "143", "144", "160", "161", "163", "164", "168", "169", "171", "172", "180", "181", "183", "184", "188", "189" ]
[ "nonn", "easy", "changed" ]
83
1
2
[ "A001620", "A001787", "A006519", "A006520", "A022560", "A136013", "A159699" ]
[ "M2344" ]
N. J. A. Sloane, Simon Plouffe
2025-04-18T21:39:10
oeisdata/seq/A006/A006520.seq
301e91bedabb4cc7f4118e9e0c02a942
A006521
Numbers n such that n divides 2^n + 1.
[ "1", "3", "9", "27", "81", "171", "243", "513", "729", "1539", "2187", "3249", "4617", "6561", "9747", "13203", "13851", "19683", "29241", "39609", "41553", "59049", "61731", "87723", "97641", "118827", "124659", "177147", "185193", "250857", "263169", "292923", "354537", "356481", "373977", "531441", "555579", "752571" ]
[ "nonn" ]
88
1
2
[ "A000051", "A006517", "A006521", "A014945", "A015973", "A057719", "A066807", "A123047", "A136473", "A327840", "A327943", "A328033", "A333429" ]
[ "M2806" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006521.seq
fb80d4f26042b1aa1d02ab4ff702c237
A006522
4-dimensional analog of centered polygonal numbers. Also number of regions created by sides and diagonals of a convex n-gon in general position.
[ "1", "0", "0", "1", "4", "11", "25", "50", "91", "154", "246", "375", "550", "781", "1079", "1456", "1925", "2500", "3196", "4029", "5016", "6175", "7525", "9086", "10879", "12926", "15250", "17875", "20826", "24129", "27811", "31900", "36425", "41416", "46904", "52921", "59500", "66675", "74481", "82954", "92131" ]
[ "nonn", "easy", "nice" ]
115
0
5
[ "A000217", "A000332", "A004006", "A006522" ]
[ "M3413" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006522.seq
45dd5314bb98676f393a2fa84ba0c6b4
A006523
Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n) for n odd.
[ "2", "240", "725760", "12454041600", "711374856192000", "102181884343418880000", "31022420086661971968000000", "17683523987479403909087232000000", "17366635237623772991036388802560000000", "27527506182452690092631959163161804800000000" ]
[ "nonn" ]
9
1
1
[ "A000142", "A006523" ]
null
N. J. A. Sloane.
2023-10-08T18:01:00
oeisdata/seq/A006/A006523.seq
6948fc5dda6c58ea7b122e0f1910ab4c
A006524
Egyptian fraction for 1/ Pi.
[ "4", "15", "609", "845029", "1010073215739", "1300459886313272270974271", "1939680952094609786557359582286462958434022504402" ]
[ "nonn", "frac" ]
38
1
1
null
[ "M3509" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:30
oeisdata/seq/A006/A006524.seq
addc9dfbdbe161792cfb4bbb65695229
A006525
Denominators of greedy Egyptian fraction for e - 2.
[ "2", "5", "55", "9999", "3620211523", "25838201785967533906", "3408847366605453091140558218322023440765" ]
[ "nonn", "frac" ]
56
1
1
[ "A001466", "A006525", "A006526", "A269993" ]
[ "M1553" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006525.seq
8e02763596006cb39d41282bcba541be
A006526
Egyptian fraction for 1/e.
[ "3", "29", "15786", "513429610", "339840390654894740", "383515880462620946584018566350380249", "226890280396768133952782550246970728734549546771915172071782710229538300" ]
[ "nonn" ]
34
0
1
[ "A006526", "A068985" ]
[ "M3122" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:30
oeisdata/seq/A006/A006526.seq
aaa4c048ddd65654a152958fe780b81c
A006527
a(n) = (n^3 + 2*n)/3.
[ "0", "1", "4", "11", "24", "45", "76", "119", "176", "249", "340", "451", "584", "741", "924", "1135", "1376", "1649", "1956", "2299", "2680", "3101", "3564", "4071", "4624", "5225", "5876", "6579", "7336", "8149", "9020", "9951", "10944", "12001", "13124", "14315", "15576", "16909", "18316", "19799", "21360", "23001", "24724", "26531", "28424", "30405" ]
[ "nonn", "easy", "nice" ]
139
0
3
[ "A000290", "A000292", "A000447", "A000578", "A002264", "A004006", "A004068", "A004126", "A004188", "A004466", "A004467", "A005843", "A005900", "A006003", "A006527", "A007588", "A054602", "A059100", "A062025", "A063521", "A063522", "A063523", "A094414", "A107735", "A135184", "A158822", "A177342", "A324999", "A327083" ]
[ "M3410" ]
N. J. A. Sloane
2024-12-29T04:45:17
oeisdata/seq/A006/A006527.seq
319013c588ca8ff30704f5d0f947e26a
A006528
a(n) = (n^4 + n^2 + 2*n)/4.
[ "0", "1", "6", "24", "70", "165", "336", "616", "1044", "1665", "2530", "3696", "5226", "7189", "9660", "12720", "16456", "20961", "26334", "32680", "40110", "48741", "58696", "70104", "83100", "97825", "114426", "133056", "153874", "177045", "202740", "231136", "262416", "296769", "334390", "375480", "420246", "468901", "521664", "578760" ]
[ "nonn", "easy" ]
72
0
3
[ "A002817", "A006528", "A343095" ]
[ "M4160" ]
N. J. A. Sloane
2023-10-11T11:26:45
oeisdata/seq/A006/A006528.seq
e0f9e6cbc346beb8434ee1b33e4fa240
A006529
(25*n^4-120*n^3+209*n^2-108*n)/6.
[ "0", "1", "10", "57", "272", "885", "2226", "4725", "8912", "15417", "24970", "38401", "56640", "80717", "111762", "151005", "199776", "259505", "331722", "418057", "520240", "640101", "779570", "940677", "1125552", "1336425", "1575626", "1845585", "2148832", "2487997", "2865810" ]
[ "nonn", "easy" ]
31
0
3
null
[ "M4717" ]
N. J. A. Sloane.
2023-06-28T20:44:42
oeisdata/seq/A006/A006529.seq
0cfb0ae6c081f5c7201bb6a68d7ab986
A006530
Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1.
[ "1", "2", "3", "2", "5", "3", "7", "2", "3", "5", "11", "3", "13", "7", "5", "2", "17", "3", "19", "5", "7", "11", "23", "3", "5", "13", "3", "7", "29", "5", "31", "2", "11", "17", "7", "3", "37", "19", "13", "5", "41", "7", "43", "11", "5", "23", "47", "3", "7", "5", "17", "13", "53", "3", "11", "7", "19", "29", "59", "5", "61", "31", "7", "2", "13", "11", "67", "17", "23", "7", "71", "3", "73", "37", "5", "19", "11", "13", "79", "5", "3", "41", "83", "7", "17", "43" ]
[ "nonn", "nice", "easy", "core" ]
224
1
2
[ "A000040", "A006530", "A020639", "A028233", "A032742", "A034684", "A034699", "A046670", "A052126", "A053585", "A061395", "A070087", "A070089", "A104350", "A124661", "A175723" ]
[ "M0428" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006530.seq
be7b1fe3df75f30148c91ae23211fbe1
A006531
Semiorders on n elements.
[ "1", "1", "3", "19", "183", "2371", "38703", "763099", "17648823", "468603091", "14050842303", "469643495179", "17315795469063", "698171064855811", "30561156525545103", "1443380517590979259", "73161586346500098903", "3961555049961803092531", "228225249142441259147103", "13938493569348563803135339" ]
[ "nonn", "nice", "easy" ]
74
0
3
[ "A000108", "A006531", "A052895" ]
[ "M3061" ]
N. J. A. Sloane
2022-06-17T16:17:07
oeisdata/seq/A006/A006531.seq
6c799384ac6f300c2398d9d8d191c58d
A006532
Numbers whose sum of divisors is a square.
[ "1", "3", "22", "66", "70", "81", "94", "115", "119", "170", "210", "214", "217", "265", "282", "310", "322", "343", "345", "357", "364", "382", "385", "400", "472", "497", "510", "517", "527", "642", "651", "679", "710", "742", "745", "782", "795", "820", "862", "884", "889", "930", "935", "966", "970", "1004", "1029", "1066", "1080", "1092", "1146" ]
[ "nonn", "nice" ]
80
1
2
[ "A000203", "A006532", "A020477", "A074385" ]
[ "M3089" ]
N. J. A. Sloane, Simon Plouffe
2022-09-08T08:44:35
oeisdata/seq/A006/A006532.seq
6d361417c8abdb4fc05ab169b73a8266
A006533
Place n equally-spaced points around a circle and join every pair of points by a chord; this divides the circle into a(n) regions.
[ "1", "2", "4", "8", "16", "30", "57", "88", "163", "230", "386", "456", "794", "966", "1471", "1712", "2517", "2484", "4048", "4520", "6196", "6842", "9109", "9048", "12951", "14014", "17902", "19208", "24158", "21510", "31931", "33888", "41449", "43826", "52956", "52992", "66712", "70034", "82993", "86840", "102091", "97776", "124314", "129448", "149986", "155894", "179447", "179280" ]
[ "nonn", "easy", "nice" ]
75
1
2
[ "A001006", "A006533", "A006561", "A006600", "A007569", "A007678", "A054726" ]
[ "M1118" ]
N. J. A. Sloane, Bjorn Poonen (poonen(AT)math.princeton.edu)
2024-12-04T11:26:48
oeisdata/seq/A006/A006533.seq
b25bb9c75da9a5ce199d26f06019eac4
A006534
Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed.
[ "1", "1", "1", "4", "6", "19", "43", "120", "307", "866", "2336", "6588", "18373", "52119", "147700", "422016", "1207477", "3471067", "9999135", "28893560", "83665729", "242826187", "706074369", "2056870697", "6001555275", "17538335077", "51323792789", "150390053432", "441210664337", "1295886453860", "3810208448847", "11214076720061", "33035788241735" ]
[ "nonn", "hard", "nice" ]
45
1
4
[ "A000577", "A001420", "A006534", "A030223", "A030224" ]
[ "M3287" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006534.seq
e54d9b80847e3204c9c64e26325f2fa6
A006535
Number of one-sided hexagonal polyominoes with n cells.
[ "1", "1", "3", "10", "33", "147", "620", "2821", "12942", "60639", "286190", "1364621", "6545430", "31586358", "153143956", "745700845", "3644379397", "17869651166", "87877879487", "433301253231", "2141584454057", "10607707971062", "52646117638427", "261756764824964", "1303625908234997", "6502430891223011", "32480041218465452", "162454295068924189", "813541940383789255", "4078750395194965720" ]
[ "nonn", "hard", "nice" ]
51
1
3
[ "A000228", "A001207", "A006535", "A030225" ]
[ "M2846" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006535.seq
87c0c37134ffd1aebd783d8760e0f38f
A006536
Switching classes of digraphs.
[ "2", "6", "38", "684", "50224", "13946352", "14061131152", "50947324188128", "666754350781269760", "31763991166456912086656", "5550343429517595744902558208", "3581353054755185129132443153728000" ]
[ "nonn", "nice" ]
20
1
1
[ "A002854", "A006536", "A049313" ]
[ "M1710" ]
N. J. A. Sloane
2022-06-17T16:19:31
oeisdata/seq/A006/A006536.seq
92fcf5809889f9766483f051830d173f
A006537
Worst cases for Pierce expansions (numerators).
[ "1", "2", "3", "4", "7", "12", "22", "30", "32", "61", "65", "115", "161", "189", "296", "470", "598", "841", "904", "1856", "2158", "2416", "1925", "3462", "2130", "3749", "6546", "11201", "2159", "2360", "5186", "6071", "8664", "14735", "59745", "68482", "117997", "175672", "268618", "135585", "178909", "314752", "490652", "76800", "116789", "125493", "290641", "540539", "831180" ]
[ "nonn", "frac" ]
30
1
2
[ "A006537", "A006538" ]
[ "M0585" ]
Jeffrey Shallit, N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006537.seq
bf2726a5292ced995c6658ed25f17906
A006538
Worst cases for Pierce expansions (denominators).
[ "1", "3", "5", "11", "11", "19", "35", "47", "53", "95", "103", "179", "251", "299", "503", "743", "1019", "1319", "1439", "2939", "3359", "3959", "5387", "5387", "5879", "5879", "17747", "17747", "23399", "23399", "23399", "23399", "23399", "23399", "93596", "186479", "186479", "278387", "442679", "493919", "493919", "493919", "830939", "1371719", "1371719", "1371719", "1371719", "1371719", "1371719" ]
[ "nonn", "frac" ]
32
1
2
[ "A006538", "A268058" ]
[ "M2471" ]
Jeffrey Shallit, N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006538.seq
a7811d4f3fbd58f057ccfa5e11bb8b77
A006539
Numerators of worst case for Engel expansion.
[ "1", "2", "4", "5", "6", "12", "18", "20", "30", "46", "60", "62", "72", "89", "105", "113", "117", "119", "120", "241", "483", "633", "647", "654", "1074", "1752", "1806", "3050", "3609", "3611", "3612", "5459", "5460", "7976", "7999", "8005", "8008", "10076", "16379" ]
[ "nonn" ]
15
0
2
null
[ "M0952" ]
Jeffrey Shallit
2015-12-17T02:56:52
oeisdata/seq/A006/A006539.seq
347754c59e203fa119e663c93f612c57
A006540
Denominators of worst case for Engel expansion.
[ "1", "3", "5", "7", "7", "13", "19", "23", "31", "47", "61", "71", "73", "121", "121", "121", "121", "121", "121", "242", "484", "661", "661", "661", "1093", "1753", "1807", "3053", "3613", "3613", "3613", "5461", "5461", "8011", "8011", "8011", "8011", "10081", "16381" ]
[ "nonn" ]
15
0
2
null
[ "M2398" ]
Jeffrey Shallit
2015-12-17T02:56:59
oeisdata/seq/A006/A006540.seq
0973b8f757e186bcc8f69921598fe919
A006541
Number of dissimilarity relations on an n-set.
[ "1", "1", "13", "4683", "102247563", "230283190977853", "81124824998504073881821", "6297562064950066033518373935334635", "144199280951655469628360978109406917583513090155", "1255482482235481041484313695469155949742941807533901307975355741" ]
[ "nonn", "nice", "easy" ]
33
1
3
[ "A000670", "A005121", "A006541" ]
[ "M4920" ]
N. J. A. Sloane
2024-12-02T14:43:39
oeisdata/seq/A006/A006541.seq
85f78efa9c4d376cede3a52fd5431509
A006542
a(n) = binomial(n,3)*binomial(n-1,3)/4.
[ "1", "10", "50", "175", "490", "1176", "2520", "4950", "9075", "15730", "26026", "41405", "63700", "95200", "138720", "197676", "276165", "379050", "512050", "681835", "896126", "1163800", "1495000", "1901250", "2395575", "2992626", "3708810", "4562425", "5573800", "6765440", "8162176", "9791320", "11682825", "13869450" ]
[ "nonn", "easy" ]
129
4
2
[ "A000012", "A000217", "A000332", "A000579", "A001263", "A002378", "A002415", "A004068", "A005585", "A005891", "A006322", "A006414", "A006542", "A006857", "A047819", "A107891", "A108679", "A114242", "A124428", "A134288", "A134289", "A134290", "A134291", "A140925", "A140935", "A169937" ]
[ "M4707" ]
N. J. A. Sloane
2025-01-07T12:57:32
oeisdata/seq/A006/A006542.seq
c4aa05213778dd4e5fe9ad9b5c1785ed
A006543
Maximal iterated binomial coefficients.
[ "1", "2", "3", "4", "5", "6", "10", "15", "45", "120", "990", "14190", "489555", "161226780", "476106503180", "19554673086218985", "698490144518203427450060", "17987097565293886931115539020016860", "1246236391932004987381133823926620650891666994820" ]
[ "nonn" ]
19
1
2
null
[ "M0512" ]
N. J. A. Sloane.
2017-08-10T18:27:15
oeisdata/seq/A006/A006543.seq
d9fdd3a43ef02ae28391dc2258c204c9
A006544
Number of stable forests with n nodes.
[ "1", "1", "2", "3", "5", "8", "15", "27", "54", "110", "238", "526", "1211", "2839", "6825", "16655", "41315", "103663", "263086", "673604", "1739155", "4521632", "11831735", "31134338", "82352098", "218837877", "584018065", "1564679863", "4207224730", "11350583175", "30718054693", "83373960954", "226907180850", "619118327796" ]
[ "nonn" ]
24
0
3
[ "A003426", "A003427", "A003428", "A003429", "A006544", "A006545" ]
[ "M0702" ]
N. J. A. Sloane.
2017-08-10T18:27:22
oeisdata/seq/A006/A006544.seq
46647756b0b94005fddcb529f7bd3208
A006545
Number of stable unicyclic graphs with n nodes.
[ "1", "2", "3", "8", "22", "62" ]
[ "nonn", "more" ]
13
3
2
[ "A003426", "A003429", "A006544", "A006545" ]
[ "M0885" ]
N. J. A. Sloane.
2017-08-10T18:27:27
oeisdata/seq/A006/A006545.seq
82f1668dc23c591856be1c77e69e54f5
A006546
Number of elements (a b, c d) in SL(2,Z) with trace n and 0 <= a <= {b, c} <= d.
[ "1", "2", "2", "3", "3", "4", "2", "8", "3", "4", "6", "8", "6", "8", "4", "10", "6", "14", "2", "18", "6", "4", "14", "18", "7", "12", "12", "22", "6", "8", "6", "31", "12", "12", "14", "28", "8", "28", "12", "18", "22", "8", "10", "26", "17", "28", "6", "50", "11", "36", "12", "18", "22", "28", "12", "44", "16", "20", "18", "52", "14", "28", "34", "28", "14", "28", "18", "72", "12" ]
[ "nonn" ]
6
3
2
null
null
John Lewis (frc.mass.edu)
2017-05-09T06:00:15
oeisdata/seq/A006/A006546.seq
26e9776216a910eae00035c5fd5fe9a9
A006547
Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).
[ "0", "2", "-20", "894", "-76936", "11218330", "-2486192988", "779417002070", "-328459055125136", "179127562413460914", "-122758432482044667940", "103274000340320165525422", "-104642430930574639703548440", "125699390463431456337149276234" ]
[ "sign" ]
7
0
2
null
null
N. J. A. Sloane.
2013-11-21T12:45:53
oeisdata/seq/A006/A006547.seq
bb058f2c95d41596813dd3faf530ea8a
A006548
(2*n)!-Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*n-1)!,i=1..n).
[ "0", "24", "480", "40320", "2903040", "479001600", "74724249600", "20922789888000", "5690998849536000", "2432902008176640000", "1021818843434188800000", "620448401733239439360000", "372269041039943663616000000" ]
[ "nonn" ]
7
1
2
null
null
N. J. A. Sloane.
2013-05-22T16:15:43
oeisdata/seq/A006/A006548.seq
762c4b8d21ce90f49827c6c4c7757fe3
A006549
Numbers k such that k and k+1 are prime powers.
[ "1", "2", "3", "4", "7", "8", "16", "31", "127", "256", "8191", "65536", "131071", "524287", "2147483647", "2305843009213693951", "618970019642690137449562111", "162259276829213363391578010288127", "170141183460469231731687303715884105727" ]
[ "nonn", "nice", "easy" ]
58
1
2
[ "A000040", "A000668", "A000961", "A006549", "A010055", "A019434", "A120431", "A164571", "A164572", "A164573", "A164574" ]
[ "M0582" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006549.seq
7628308f313da6e32bd3291610ad3b65
A006550
n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).
[ "0", "1", "10", "57", "234", "770", "2136", "5180", "11292", "22599", "42190", "74371", "124950", "201552", "313964", "474510", "698456", "1004445", "1414962", "1956829", "2661730", "3566766", "4715040", "6156272", "7947444", "10153475", "12847926", "16113735", "20043982", "24742684", "30325620" ]
[ "nonn" ]
34
1
3
null
null
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006550.seq
f262b4bb117e9b350d9f3ccbaefdffb3
A006551
Maximal Eulerian numbers.
[ "1", "1", "4", "11", "66", "302", "2416", "15619", "156190", "1310354", "15724248", "162512286", "2275172004", "27971176092", "447538817472", "6382798925475", "114890380658550", "1865385657780650", "37307713155613000", "679562217794156938", "14950368791471452636" ]
[ "nonn" ]
48
1
3
[ "A006551", "A008292", "A025585", "A180056" ]
[ "M3426" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2024-12-20T11:07:17
oeisdata/seq/A006/A006551.seq
245efd6fbf582d38975ceedf389382e6
A006552
Numbers k such that k*3^k + 1 is prime.
[ "2", "8", "32", "54", "114", "414", "1400", "1850", "2848", "4874", "7268", "19290", "337590", "1183414" ]
[ "nonn", "hard" ]
33
1
1
null
[ "M1848" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006552.seq
c0b5d300699ffc00ad197c09bbb223f7
A006553
Numbers k such that k*3^k - 1 is prime.
[ "1", "2", "6", "10", "18", "40", "46", "86", "118", "170", "1172", "1698", "1810", "2268", "4338", "18362", "72662", "88392", "94110", "161538", "168660", "292340", "401208", "560750", "1035092" ]
[ "hard", "nonn" ]
35
1
2
null
[ "M1575" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006553.seq
1c2809278398267d51d08b3b628bf1f9
A006554
Minimal discriminant of totally real number field of degree n.
[ "1", "5", "49", "725", "14641", "300125", "20134393", "282300416", "9685993193" ]
[ "nonn", "nice" ]
17
1
2
null
[ "M4006" ]
N. J. A. Sloane
2021-12-18T20:52:57
oeisdata/seq/A006/A006554.seq
90cdc8921fbe8907ff169361c8a14f6b
A006555
Minimal absolute value of discriminants of number fields of degree n with exactly 2 (1 pair of) complex embeddings.
[ "3", "23", "275", "4511", "92779", "2306599" ]
[ "nonn", "hard", "more" ]
38
2
1
[ "A006554", "A006555", "A343290" ]
[ "M3103" ]
N. J. A. Sloane.
2021-05-17T02:02:51
oeisdata/seq/A006/A006555.seq
412887ed242dab4240735699765ba987
A006556
Number of different cycles of digits in the decimal expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2 or 5.
[ "2", "1", "5", "2", "1", "1", "1", "1", "2", "12", "8", "2", "1", "4", "1", "1", "2", "2", "9", "6", "2", "2", "1", "25", "3", "2", "1", "1", "3", "1", "17", "3", "1", "2", "2", "2", "1", "4", "1", "1", "2", "1", "2", "2", "7", "1", "2", "1", "1", "34", "8", "5", "1", "1", "1", "54", "4", "10", "2", "2", "2", "2", "1", "4", "3", "1", "2", "3", "11", "2", "1", "2", "1", "1", "1", "4", "2", "2", "1", "3", "2", "1", "2", "2", "14", "3", "1", "3", "2", "2", "1", "1", "1", "1", "1", "10", "2", "1", "6" ]
[ "nonn", "easy", "base", "nice" ]
29
3
1
[ "A002371", "A006556", "A048595", "A054471" ]
[ "M0175" ]
N. J. A. Sloane
2020-05-27T20:49:43
oeisdata/seq/A006/A006556.seq
6175f94efe6e2f99364e6762dc861510
A006557
Minimal absolute value of discriminants of number fields of degree n.
[ "1", "3", "23", "117", "1609", "9747", "184607", "1257728" ]
[ "nonn", "hard", "more" ]
22
1
2
[ "A006557", "A343690", "A343772" ]
[ "M3099" ]
N. J. A. Sloane.
2021-04-30T21:35:04
oeisdata/seq/A006/A006557.seq
4a4f01f2b15408f6c783f609c4c72c35
A006558
Start of first run of n consecutive integers with same number of divisors.
[ "1", "2", "33", "242", "11605", "28374", "171893", "1043710445721", "2197379769820", "2642166652554075" ]
[ "nonn", "more", "hard" ]
141
1
2
[ "A000005", "A005237", "A005238", "A006558", "A006601", "A019273", "A034173", "A039665", "A049051", "A115158", "A119479" ]
[ "M2155" ]
N. J. A. Sloane, Robert G. Wilson v
2024-02-08T07:10:53
oeisdata/seq/A006/A006558.seq
0c590d932e58e38e3b1dafda73de485f
A006559
Short period primes: the decimal expansion of 1/p has period less than p-1, but greater than zero.
[ "3", "11", "13", "31", "37", "41", "43", "53", "67", "71", "73", "79", "83", "89", "101", "103", "107", "127", "137", "139", "151", "157", "163", "173", "191", "197", "199", "211", "227", "239", "241", "251", "271", "277", "281", "283", "293", "307", "311", "317", "331", "347", "349", "353", "359", "373", "397", "401", "409", "421", "431", "439", "443", "449", "457" ]
[ "nonn", "easy", "nice", "base" ]
38
1
1
[ "A006559", "A006883" ]
[ "M2881" ]
N. J. A. Sloane
2025-03-03T19:10:57
oeisdata/seq/A006/A006559.seq
67224745f73f8abede37edca3b88fa15
A006560
Smallest starting prime for n consecutive primes in arithmetic progression.
[ "2", "2", "3", "251", "9843019", "121174811" ]
[ "nonn", "hard", "more", "nice" ]
83
1
1
[ "A005115", "A006560", "A006562", "A033451", "A052239", "A052243", "A054800", "A058362", "A059044", "A089180", "A093364", "A126989", "A210727" ]
[ "M0927" ]
N. J. A. Sloane
2023-04-03T10:36:09
oeisdata/seq/A006/A006560.seq
eb60d7d58055c157197c0634bc6dfd3a
A006561
Number of intersections of diagonals in the interior of a regular n-gon.
[ "0", "0", "0", "1", "5", "13", "35", "49", "126", "161", "330", "301", "715", "757", "1365", "1377", "2380", "1837", "3876", "3841", "5985", "5941", "8855", "7297", "12650", "12481", "17550", "17249", "23751", "16801", "31465", "30913", "40920", "40257", "52360", "46981", "66045", "64981", "82251", "80881", "101270", "84841", "123410", "121441" ]
[ "easy", "nonn", "nice" ]
158
1
5
[ "A001006", "A006533", "A006561", "A006600", "A007569", "A007678", "A054726", "A101363", "A290447", "A292104", "A292105" ]
[ "M3833" ]
N. J. A. Sloane, Bjorn Poonen (poonen(AT)math.princeton.edu)
2023-11-07T16:14:24
oeisdata/seq/A006/A006561.seq
cab2dc50220522a01157e420574815d8
A006562
Balanced primes (of order one): primes which are the average of the previous prime and the following prime.
[ "5", "53", "157", "173", "211", "257", "263", "373", "563", "593", "607", "653", "733", "947", "977", "1103", "1123", "1187", "1223", "1367", "1511", "1747", "1753", "1907", "2287", "2417", "2677", "2903", "2963", "3307", "3313", "3637", "3733", "4013", "4409", "4457", "4597", "4657", "4691", "4993", "5107", "5113", "5303", "5387", "5393" ]
[ "nonn", "easy", "nice" ]
173
1
1
[ "A000040", "A006560", "A006562", "A036263", "A046869", "A051634", "A051635", "A051795", "A054342", "A055380", "A064113", "A075540", "A081415", "A082077", "A082078", "A082079", "A096693", "A096697", "A096698", "A096699", "A096700", "A096701", "A096702", "A096703", "A096704", "A096710", "A117078", "A117563", "A117876", "A125576", "A125830", "A173891", "A173892", "A173893", "A178943", "A225494" ]
[ "M4011" ]
N. J. A. Sloane and Robert G. Wilson v
2025-03-02T19:26:02
oeisdata/seq/A006/A006562.seq
d72140c5a62d19968c12560eadc3f07d
A006563
(2*n)!-Sum ((-1)^(i+1)*binomial(n,i)*2^i*(2*i-1)!,i=1..n).
[ "1", "0", "44", "-174", "117256", "-7589530", "2965194588", "-692238710870", "349381845013136", "-172725188707732914", "125191334490221307940", "-102149999612542557845422", "105262879332307879142908440", "-125296099002304850701565276234" ]
[ "sign" ]
6
0
3
null
null
N. J. A. Sloane.
2012-03-30T16:45:01
oeisdata/seq/A006/A006563.seq
f421e6e6cf3593d9fb102283471427db
A006564
Icosahedral numbers: a(n) = n*(5*n^2 - 5*n + 2)/2.
[ "1", "12", "48", "124", "255", "456", "742", "1128", "1629", "2260", "3036", "3972", "5083", "6384", "7890", "9616", "11577", "13788", "16264", "19020", "22071", "25432", "29118", "33144", "37525", "42276", "47412", "52948", "58899", "65280", "72106", "79392", "87153", "95404", "104160", "113436", "123247", "133608" ]
[ "nonn", "nice", "easy" ]
90
1
2
[ "A000292", "A000566", "A000578", "A005900", "A006564", "A006566", "A053012", "A175578" ]
[ "M4837" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006564.seq
d09f1341502a1ede13e42eb193c9e749
A006565
Number of ways to color vertices of a hexagon using <= n colors, allowing only rotations.
[ "0", "1", "14", "130", "700", "2635", "7826", "19684", "43800", "88725", "166870", "295526", "498004", "804895", "1255450", "1899080", "2796976", "4023849", "5669790", "7842250", "10668140", "14296051", "18898594", "24674860", "31853000", "40692925", "51489126", "64573614" ]
[ "nonn" ]
37
0
3
[ "A006565", "A027670", "A075195" ]
[ "M4942" ]
N. J. A. Sloane.
2025-03-21T11:15:51
oeisdata/seq/A006/A006565.seq
bac403147cfc2e7d11774d1d4e4fdc3e
A006566
Dodecahedral numbers: a(n) = n*(3*n - 1)*(3*n - 2)/2.
[ "0", "1", "20", "84", "220", "455", "816", "1330", "2024", "2925", "4060", "5456", "7140", "9139", "11480", "14190", "17296", "20825", "24804", "29260", "34220", "39711", "45760", "52394", "59640", "67525", "76076", "85320", "95284", "105995", "117480", "129766", "142880", "156849", "171700", "187460", "204156" ]
[ "nonn", "easy", "nice" ]
126
0
3
[ "A000292", "A000578", "A005900", "A006564", "A006566", "A027907", "A035006", "A060544", "A093485", "A124388", "A228887", "A228888", "A295421" ]
[ "M5089" ]
N. J. A. Sloane
2024-01-09T08:47:29
oeisdata/seq/A006/A006566.seq
076186264ed7e1daf7b065707d079977
A006567
Emirps (primes whose reversal is a different prime).
[ "13", "17", "31", "37", "71", "73", "79", "97", "107", "113", "149", "157", "167", "179", "199", "311", "337", "347", "359", "389", "701", "709", "733", "739", "743", "751", "761", "769", "907", "937", "941", "953", "967", "971", "983", "991", "1009", "1021", "1031", "1033", "1061", "1069", "1091", "1097", "1103", "1109", "1151", "1153", "1181", "1193", "1201" ]
[ "nonn", "nice", "easy", "base", "changed" ]
86
1
1
[ "A002385", "A003684", "A004086", "A006567", "A007500", "A007628", "A046732", "A048051", "A048052", "A048053", "A048054", "A048895" ]
[ "M4887" ]
N. J. A. Sloane
2025-04-14T18:17:34
oeisdata/seq/A006/A006567.seq
ae4dea5e7d992e7ffd8baa66936d2403
A006568
Denominators of generalized Bernoulli numbers.
[ "1", "3", "18", "90", "270", "1134", "5670", "2430", "7290", "133650", "112266", "1990170", "9950850", "2296350", "984150", "117113850", "351341550", "33657930", "21597171750", "3410079750", "572893398", "33613643250", "834229509750", "108812544750", "544062723750", "18280507518", "105464466450", "18690647109750" ]
[ "nonn", "frac" ]
52
0
2
[ "A006568", "A006569", "A132092", "A132099", "A209518" ]
[ "M3046" ]
N. J. A. Sloane
2024-01-24T08:49:11
oeisdata/seq/A006/A006568.seq
6a218b67098ebfa0e9f4879e62e5ab99
A006569
Numerators of generalized Bernoulli numbers.
[ "1", "-1", "1", "1", "-1", "-5", "-1", "7", "13", "-307", "-479", "1837", "100921", "15587", "-23737", "-5729723", "14731223", "9129833", "2722952839", "-4700745901", "-1556262845", "190717213397", "24684889339847", "-50242799489", "-148437433077277", "-8592042383621", "221844330989749", "176585172615885307", "-9245931549625447" ]
[ "frac", "sign", "easy" ]
40
0
6
[ "A006568", "A006569", "A132092", "A132099" ]
[ "M3731" ]
N. J. A. Sloane
2024-01-24T08:49:23
oeisdata/seq/A006/A006569.seq
8b56e45b1c14cc7fe38206e01cbe0e14
A006570
From trees with valency <= 3.
[ "1", "2", "5", "15", "48", "166", "596", "2221", "8472", "32995", "130507", "523100", "2119454", "8667529", "35727261", "148285069", "619172847", "2599212499", "10963049307", "46437309218", "197454056586", "842504023722", "3606195947971", "15480329150558", "66628688247862", "287475949517326", "1243140817965661" ]
[ "nonn" ]
25
1
2
null
[ "M1475" ]
N. J. A. Sloane.
2019-10-23T08:10:17
oeisdata/seq/A006/A006570.seq
664deea2d04da86b5ab96e6bf7186d2f
A006571
Expansion of q*Product_{k>=1} (1-q^k)^2*(1-q^(11*k))^2.
[ "1", "-2", "-1", "2", "1", "2", "-2", "0", "-2", "-2", "1", "-2", "4", "4", "-1", "-4", "-2", "4", "0", "2", "2", "-2", "-1", "0", "-4", "-8", "5", "-4", "0", "2", "7", "8", "-1", "4", "-2", "-4", "3", "0", "-4", "0", "-8", "-4", "-6", "2", "-2", "2", "8", "4", "-3", "8", "2", "8", "-6", "-10", "1", "0", "0", "0", "5", "-2", "12", "-14", "4", "-8", "4", "2", "-7", "-4", "1", "4", "-3", "0", "4", "-6", "4", "0", "-2", "8", "-10", "-4", "1", "16", "-6", "4", "-2", "12", "0", "0", "15", "4", "-8", "-2", "-7", "-16", "0", "-8", "-7", "6", "-2", "-8" ]
[ "sign", "easy", "nice", "mult" ]
88
1
2
[ "A002070", "A006571", "A030200", "A032442" ]
[ "M0092" ]
N. J. A. Sloane
2024-09-14T06:54:16
oeisdata/seq/A006/A006571.seq
093dd23d06e7e886b8f8711380bf59a2
A006572
Numerators of an asymptotic expansion for the number of forests on n nodes (A001858).
[ "0", "0", "1", "5", "11", "-203", "-17207", "-3607", "1408301", "8181503", "-3299598169", "-14983154641", "-449428440959", "2480887997789", "19076621521399973", "-31806561859970819", "-3485566370059659659", "-2180443004193000007", "54188073629843061671671" ]
[ "sign", "frac" ]
17
0
4
[ "A001858", "A006572", "A006573", "A111999" ]
[ "M3817" ]
N. J. A. Sloane.
2017-05-11T11:47:57
oeisdata/seq/A006/A006572.seq
455c644122cc986fbc5a412197e14348
A006573
Denominators of an asymptotic expansion for the number of forests on n nodes (A001858).
[ "1", "1", "1", "2", "8", "16", "384", "768", "3072", "6144", "1474560", "589824", "11796480", "7864320", "11890851840", "23781703680", "95126814720", "27179089920", "91321742131200", "7305739370496", "730573937049600", "1461147874099200", "385743038762188800", "771486077524377600" ]
[ "nonn", "frac" ]
13
0
4
[ "A001858", "A006572", "A006573", "A111999" ]
[ "M1828" ]
N. J. A. Sloane.
2017-05-11T11:48:08
oeisdata/seq/A006/A006573.seq
7697e8233049b5427b7c26df3434dff2
A006574
Number of domino n-tuples.
[ "2", "5", "14", "38", "107" ]
[ "nonn" ]
12
1
1
null
[ "M1454" ]
N. J. A. Sloane.
2012-03-30T16:45:01
oeisdata/seq/A006/A006574.seq
4c582d9bb83c8d1e0804cb4b081e8199
A006575
Number of primitive (aperiodic, or Lyndon) asymmetric rhythm cycles: ones having no nontrivial shift automorphism.
[ "1", "2", "4", "10", "24", "60", "156", "410", "1092", "2952", "8052", "22140", "61320", "170820", "478288", "1345210", "3798240", "10761660", "30585828", "87169608", "249055976", "713205900", "2046590844", "5883948540", "16945772184", "48882035160", "141214767876" ]
[ "nonn" ]
40
1
2
[ "A006575", "A098691", "A133267" ]
[ "M1204" ]
N. J. A. Sloane
2021-12-26T21:36:57
oeisdata/seq/A006/A006575.seq
106b39b7d7129dd79a6fa414365f1a9e
A006576
Primitive repfigit numbers.
[ "14", "19", "47", "61", "75", "197", "742", "1104", "1537", "2580", "3684", "4788", "7385", "7647", "7909", "31331", "34285", "34348", "55604", "86935", "120284", "129106", "147640", "156146", "174680", "183186", "298320" ]
[ "nonn", "base" ]
15
1
1
[ "A006576", "A007629" ]
[ "M4923" ]
N. J. A. Sloane.
2017-05-12T00:52:32
oeisdata/seq/A006/A006576.seq
75b10344ddd34b06c66ee3f154e8dc8f
A006577
Number of halving and tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.
[ "0", "1", "7", "2", "5", "8", "16", "3", "19", "6", "14", "9", "9", "17", "17", "4", "12", "20", "20", "7", "7", "15", "15", "10", "23", "10", "111", "18", "18", "18", "106", "5", "26", "13", "13", "21", "21", "21", "34", "8", "109", "8", "29", "16", "16", "16", "104", "11", "24", "24", "24", "11", "11", "112", "112", "19", "32", "19", "32", "19", "19", "107", "107", "6", "27", "27", "27", "14", "14", "14", "102", "22" ]
[ "nonn", "nice", "easy", "hear", "look" ]
228
1
3
[ "A006370", "A006577", "A008884", "A008908", "A025586", "A070165", "A112695", "A125731", "A127885", "A127886", "A135282", "A161021", "A161022", "A161023", "A208981" ]
[ "M4323" ]
N. J. A. Sloane, Bill Gosper
2025-02-16T08:32:30
oeisdata/seq/A006/A006577.seq
95dea8fc1eb805a450f3a2bdd57a6404
A006578
Triangular numbers plus quarter squares: n*(n+1)/2 + floor(n^2/4) (i.e., A000217(n) + A002620(n)).
[ "0", "1", "4", "8", "14", "21", "30", "40", "52", "65", "80", "96", "114", "133", "154", "176", "200", "225", "252", "280", "310", "341", "374", "408", "444", "481", "520", "560", "602", "645", "690", "736", "784", "833", "884", "936", "990", "1045", "1102", "1160", "1220", "1281", "1344", "1408", "1474", "1541", "1610", "1680", "1752", "1825", "1900", "1976", "2054" ]
[ "nonn", "easy" ]
139
0
3
[ "A000034", "A001859", "A002378", "A002620", "A002717", "A006578", "A032766", "A051125", "A070893", "A077043", "A104567" ]
[ "M3329" ]
N. J. A. Sloane
2023-08-23T08:35:12
oeisdata/seq/A006/A006578.seq
87f17b00a12516ea0cfd536031d7a4a0
A006579
a(n) = Sum_{k=1..n-1} gcd(n,k).
[ "0", "1", "2", "4", "4", "9", "6", "12", "12", "17", "10", "28", "12", "25", "30", "32", "16", "45", "18", "52", "44", "41", "22", "76", "40", "49", "54", "76", "28", "105", "30", "80", "72", "65", "82", "132", "36", "73", "86", "140", "40", "153", "42", "124", "144", "89", "46", "192", "84", "145", "114", "148", "52", "189", "134", "204", "128", "113", "58", "300", "60", "121", "210", "192" ]
[ "nonn" ]
61
1
3
[ "A003989", "A006579", "A018804" ]
[ "M0941" ]
Marc LeBrun
2023-04-26T06:20:25
oeisdata/seq/A006/A006579.seq
d3cd9cb1982b63176ebfb0c1f1216816
A006580
a(n) = Sum_{k=1..n-1} lcm(k,n-k).
[ "0", "0", "1", "4", "8", "20", "21", "56", "60", "96", "105", "220", "152", "364", "301", "360", "464", "816", "549", "1140", "760", "1036", "1221", "2024", "1196", "2200", "2041", "2484", "2184", "4060", "2205", "4960", "3664", "4224", "4641", "5180", "4008", "8436", "6517", "7072", "5980", "11480", "6321", "13244", "8888", "9540", "11661", "17296" ]
[ "nonn" ]
49
0
4
[ "A000010", "A003990", "A006580", "A023900", "A057660", "A130054", "A209295" ]
[ "M3336" ]
N. J. A. Sloane
2023-04-28T08:16:56
oeisdata/seq/A006/A006580.seq
f3a42a34d86f97ce439d12787e335bf8
A006581
a(n) = Sum_{k=1..n-1} (k AND n-k).
[ "1", "0", "4", "4", "5", "0", "12", "16", "21", "16", "24", "20", "17", "0", "32", "48", "65", "64", "84", "84", "85", "64", "92", "96", "101", "80", "88", "68", "49", "0", "80", "128", "177", "192", "244", "260", "277", "256", "316", "336", "357", "336", "360", "340", "321", "256", "336", "368", "401", "384", "420", "404", "389", "320", "364", "352", "341", "272", "264", "196" ]
[ "nonn" ]
34
2
3
[ "A000292", "A003985", "A006581", "A090889" ]
[ "M3225" ]
N. J. A. Sloane
2023-05-08T02:01:35
oeisdata/seq/A006/A006581.seq
8d8f82f96412ebd37f00200cdff094ce
A006582
a(n) = Sum_{k=1..n-1} k XOR n-k.
[ "0", "6", "4", "12", "20", "42", "32", "40", "48", "78", "84", "116", "148", "210", "176", "176", "176", "214", "212", "252", "292", "378", "368", "408", "448", "542", "580", "676", "772", "930", "832", "800", "768", "806", "772", "812", "852", "970", "928", "968", "1008", "1134", "1172", "1300", "1428", "1650", "1584", "1616", "1648", "1782", "1812", "1948" ]
[ "nonn" ]
37
2
2
[ "A003987", "A006582" ]
[ "M4053" ]
N. J. A. Sloane
2023-05-08T02:02:38
oeisdata/seq/A006/A006582.seq
0994d67a1b68049ce54f28195fbc5aac
A006583
a(n) = Sum_{k=1..n-1} (k OR n-k).
[ "1", "6", "8", "16", "25", "42", "44", "56", "69", "94", "108", "136", "165", "210", "208", "224", "241", "278", "296", "336", "377", "442", "460", "504", "549", "622", "668", "744", "821", "930", "912", "928", "945", "998", "1016", "1072", "1129", "1226", "1244", "1304" ]
[ "nonn", "base" ]
36
2
2
[ "A003986", "A006583" ]
[ "M4069" ]
N. J. A. Sloane
2023-05-08T03:24:45
oeisdata/seq/A006/A006583.seq
3642727f5e0c7e83357d744c7c4069ac
A006584
If n mod 2 = 0 then n*(n^2-4)/12 else n*(n^2-1)/12.
[ "0", "0", "0", "2", "4", "10", "16", "28", "40", "60", "80", "110", "140", "182", "224", "280", "336", "408", "480", "570", "660", "770", "880", "1012", "1144", "1300", "1456", "1638", "1820", "2030", "2240", "2480", "2720", "2992", "3264", "3570", "3876", "4218", "4560", "4940", "5320" ]
[ "nonn", "easy" ]
59
0
4
[ "A000027", "A003451", "A006584", "A006918", "A027656", "A034877", "A110660" ]
null
N. J. A. Sloane
2022-09-17T03:44:06
oeisdata/seq/A006/A006584.seq
ff0ef8ddb50e926f422e05b9e6eacb79
A006585
Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
[ "1", "0", "1", "6", "72", "2320", "245765", "151182379" ]
[ "nonn", "nice", "hard", "more" ]
51
1
4
[ "A000058", "A002966", "A002967", "A006585", "A280518" ]
[ "M4281" ]
N. J. A. Sloane
2024-02-21T10:50:55
oeisdata/seq/A006/A006585.seq
d126d7a259165638ee582be8fe5f0be1
A006586
a(n) = Sum_{k=1..n} floor((2n-1)/(2k+1)).
[ "1", "2", "4", "6", "8", "10", "14", "15", "18", "22", "24", "27", "31", "33", "37", "40", "44", "47", "51", "53", "57", "63", "65", "68", "73", "75", "81", "85", "87", "91", "97", "100", "104", "108", "112", "115", "121", "125", "129", "134", "136", "142", "146", "148", "156", "160", "164", "166", "173", "176", "180", "188", "190", "194", "200", "202", "208", "214", "218", "223", "227" ]
[ "nonn", "easy" ]
40
2
2
null
[ "M0988" ]
N. J. A. Sloane
2024-09-02T01:20:40
oeisdata/seq/A006/A006586.seq
1e3f11472403733e939a112f634c145c
A006587
a(n) = 3*2^(2*n)*(3*n)!/((2*n)!*n!).
[ "3", "36", "720", "16128", "380160", "9225216", "228114432", "5715394560", "144599482368", "3685869158400", "94513444945920", "2435255516528640", "62999001405849600", "1635260233414606848", "42568679092062781440", "1110895735754245275648" ]
[ "nonn" ]
22
0
1
null
null
N. J. A. Sloane
2024-07-25T08:43:06
oeisdata/seq/A006/A006587.seq
0fa4ecab8141c25fd6423b2a089d223d
A006588
a(n) = 4^n*(3*n)!/((2*n)!*n!).
[ "1", "12", "240", "5376", "126720", "3075072", "76038144", "1905131520", "48199827456", "1228623052800", "31504481648640", "811751838842880", "20999667135283200", "545086744471535616", "14189559697354260480", "370298578584748425216", "9684502341534993088512", "253765034617761850982400" ]
[ "nonn", "easy", "nice" ]
49
0
2
[ "A000302", "A005809", "A006588", "A013609" ]
null
N. J. A. Sloane
2024-12-29T04:45:13
oeisdata/seq/A006/A006588.seq
9d45f20107eaedc6f46a222a32a0d35e
A006589
a(n) = (n+3)*2^n - 1.
[ "0", "2", "7", "19", "47", "111", "255", "575", "1279", "2815", "6143", "13311", "28671", "61439", "131071", "278527", "589823", "1245183", "2621439", "5505023", "11534335", "24117247", "50331647", "104857599", "218103807", "452984831", "939524095" ]
[ "nonn", "easy" ]
33
-1
2
[ "A001792", "A006589", "A045623", "A173786" ]
null
N. J. A. Sloane
2025-02-06T15:13:18
oeisdata/seq/A006/A006589.seq
379817448a00770abbefc4f9e2ea7ddf
A006590
a(n) = Sum_{k=1..n} ceiling(n/k).
[ "1", "3", "6", "9", "13", "16", "21", "24", "29", "33", "38", "41", "48", "51", "56", "61", "67", "70", "77", "80", "87", "92", "97", "100", "109", "113", "118", "123", "130", "133", "142", "145", "152", "157", "162", "167", "177", "180", "185", "190", "199", "202", "211", "214", "221", "228", "233", "236", "247", "251", "258", "263", "270", "273", "282", "287", "296", "301" ]
[ "nonn", "nice", "easy" ]
42
1
2
[ "A000005", "A006218", "A006590" ]
[ "M2522" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006590.seq
414c3e4c6fc1edab768670cfc742bf72
A006591
a(n) = Sum_{k=1..n} nearest integer to n/k (if n/k is midway between two numbers take the smaller).
[ "1", "3", "5", "8", "11", "14", "17", "22", "24", "28", "33", "36", "40", "45", "48", "53", "57", "62", "66", "71", "74", "79", "86", "89", "93", "99", "102", "109", "114", "117", "122", "129", "133", "138", "143", "148", "152", "159", "164", "169", "175", "178", "185", "190", "193", "202", "207", "212", "215", "223", "227", "232", "241", "244", "249", "256", "259", "266", "273" ]
[ "nonn", "easy" ]
16
1
2
[ "A006218", "A006591" ]
[ "M2434" ]
N. J. A. Sloane.
2022-02-08T17:06:59
oeisdata/seq/A006/A006591.seq
7d10546805e3d31efee9e6ea8246ab18
A006592
a(n) = 10*n^3 - 6*n^2.
[ "0", "4", "56", "216", "544", "1100", "1944", "3136", "4736", "6804", "9400", "12584", "16416", "20956", "26264", "32400", "39424", "47396", "56376", "66424", "77600", "89964", "103576", "118496", "134784", "152500", "171704", "192456", "214816", "238844", "264600", "292144", "321536", "352836", "386104", "421400", "458784", "498316", "540056" ]
[ "easy", "nonn" ]
32
0
2
null
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006592.seq
51cae5137be304c12780c887c51aec71
A006593
Least number which is side of n Pythagorean triples.
[ "3", "5", "16", "12", "15", "125", "24", "40", "75", "48", "80", "72", "84", "60", "65536", "192", "144", "524288", "384", "640", "9375", "168", "120", "300", "1536", "520", "576", "3072", "975", "2147483648", "336", "240", "1171875", "1500", "1040", "137438953472", "504", "360", "600", "672", "420", "4608", "50000", "780", "3456", "196608", "9216" ]
[ "nonn" ]
42
1
1
[ "A006593", "A046081" ]
[ "M2499" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006593.seq
bda2643fe7a8133e5f9dadb5c5fd8118
A006594
A Beatty sequence: [ n(1 + 1/e) ].
[ "1", "2", "4", "5", "6", "8", "9", "10", "12", "13", "15", "16", "17", "19", "20", "21", "23", "24", "25", "27", "28", "30", "31", "32", "34", "35", "36", "38", "39", "41", "42", "43", "45", "46", "47", "49", "50", "51", "53", "54", "56", "57", "58", "60", "61", "62", "64", "65", "67", "68", "69", "71", "72", "73", "75", "76", "77", "79", "80", "82", "83", "84", "86", "87", "88", "90", "91", "93", "94", "95", "97" ]
[ "nonn" ]
18
1
2
[ "A000572", "A006594" ]
[ "M0947" ]
N. J. A. Sloane.
2017-06-30T01:49:01
oeisdata/seq/A006/A006594.seq
3c3f1149a427add2d12744882221f58e
A006595
a(n) = (n+2)!/4 + n!/2.
[ "1", "2", "7", "33", "192", "1320", "10440", "93240", "927360", "10160640", "121564800", "1576713600", "22034073600", "330032102400", "5274286617600", "89575694208000", "1611054821376000", "30589118816256000", "611426688897024000", "12833558093131776000", "282216632948490240000" ]
[ "nonn", "easy" ]
36
0
2
[ "A006595", "A059418" ]
[ "M1794" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006595.seq
83c9b6c77d25791f0c2d27e096c65e2a
A006596
Numbers k such that (2^(2k+1) - 2^(k+1) + 1)/5 is prime.
[ "2", "5", "6", "14", "21", "26", "141", "278", "281", "306", "345", "1365", "2573", "2661", "4766", "5385" ]
[ "nonn", "hard", "more" ]
24
1
1
null
[ "M1325" ]
N. J. A. Sloane
2023-06-28T14:36:51
oeisdata/seq/A006/A006596.seq
48fd2f9e453ae08c3a3ea79b5fec9665
A006597
a(n) = n^2*(5*n-3)/2.
[ "0", "1", "14", "54", "136", "275", "486", "784", "1184", "1701", "2350", "3146", "4104", "5239", "6566", "8100", "9856", "11849", "14094", "16606", "19400", "22491", "25894", "29624", "33696", "38125", "42926", "48114", "53704", "59711", "66150", "73036", "80384", "88209", "96526", "105350", "114696", "124579", "135014", "146016" ]
[ "nonn", "easy" ]
43
0
3
[ "A006597", "A100145", "A100177", "A262000" ]
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006597.seq
486784e0ab1b044337187bfabe2909da
A006598
Numbers n such that 2^(2n+1) - 2^(n+1) + 1 is a prime.
[ "1", "3", "23", "36", "39", "56", "75", "83", "119", "120", "176", "183", "228", "683", "1520" ]
[ "nonn" ]
22
1
2
[ "A006598", "A007670", "A092440", "A325914" ]
[ "M3098" ]
N. J. A. Sloane, Robert G. Wilson v
2019-09-13T20:43:59
oeisdata/seq/A006/A006598.seq
7f294f33b2f3bf9716dc553a4a4884e7
A006599
Numbers k such that 2^(2k+1) + 2^(k+1) + 1 is prime.
[ "0", "1", "2", "5", "9", "14", "78", "81", "141", "189", "498", "5070", "7349", "38645", "42618", "53346" ]
[ "nonn", "more" ]
33
1
3
[ "A006599", "A108062" ]
[ "M1358" ]
N. J. A. Sloane.
2025-01-03T18:44:15
oeisdata/seq/A006/A006599.seq
1a3fea38d1667920518a639e52b1dc32
A006600
Total number of triangles visible in regular n-gon with all diagonals drawn.
[ "1", "8", "35", "110", "287", "632", "1302", "2400", "4257", "6956", "11297", "17234", "25935", "37424", "53516", "73404", "101745", "136200", "181279", "236258", "306383", "389264", "495650", "620048", "772785", "951384", "1167453", "1410350", "1716191", "2058848", "2463384", "2924000", "3462305", "4067028", "4776219", "5568786", "6479551" ]
[ "nonn", "easy", "nice" ]
50
3
2
[ "A001006", "A005732", "A006533", "A006561", "A006600", "A007569", "A007678", "A054726", "A203016", "A260417", "A363174" ]
[ "M4513" ]
N. J. A. Sloane
2024-11-26T10:06:27
oeisdata/seq/A006/A006600.seq
39fc51f08b13f36e5896bf04fe08bdd7