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1999-12-11 03:00:00
2025-04-28 00:58:08
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A005101
Abundant numbers (sum of divisors of m exceeds 2m).
[ "12", "18", "20", "24", "30", "36", "40", "42", "48", "54", "56", "60", "66", "70", "72", "78", "80", "84", "88", "90", "96", "100", "102", "104", "108", "112", "114", "120", "126", "132", "138", "140", "144", "150", "156", "160", "162", "168", "174", "176", "180", "186", "192", "196", "198", "200", "204", "208", "210", "216", "220", "222", "224", "228", "234", "240", "246", "252", "258", "260", "264", "270" ]
[ "nonn", "easy", "core", "nice" ]
163
1
1
[ "A000396", "A001065", "A005100", "A005101", "A005231", "A005835", "A006038", "A080224", "A091191", "A091194", "A091196", "A094268", "A173490", "A302991" ]
[ "M4825" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005101.seq
79c0735400701632c8a54bc73eb62aec
A005102
Minimal determinant of any n-dimensional norm 2 lattice.
[ "1", "2", "3", "4", "4", "4", "3", "2", "1", "2", "3", "2", "1", "2", "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", "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" ]
[ "nonn" ]
12
0
2
null
[ "M0445" ]
N. J. A. Sloane
2023-10-26T22:36:30
oeisdata/seq/A005/A005102.seq
e13b7d7d2af3b9a619847f7ca35de67f
A005103
Minimal determinant of n-dimensional norm 3 lattice.
[ "1", "3", "8", "16", "32", "48", "64", "64" ]
[ "nonn", "more", "hard" ]
26
0
2
null
[ "M2724" ]
N. J. A. Sloane
2023-10-26T23:16:10
oeisdata/seq/A005/A005103.seq
f6648787b3ff2fbfc72b57a880573777
A005104
Minimal determinant of n-dimensional norm 4 lattice.
[ "1", "4", "12", "32", "64", "128", "192", "256", "256" ]
[ "nonn", "more", "hard" ]
13
0
2
null
[ "M3442" ]
N. J. A. Sloane
2023-10-26T22:40:36
oeisdata/seq/A005/A005104.seq
c8c2b4e2dffecd42c0279c13d52462d8
A005105
Class 1+ primes: primes of the form 2^i*3^j - 1 with i, j >= 0.
[ "2", "3", "5", "7", "11", "17", "23", "31", "47", "53", "71", "107", "127", "191", "383", "431", "647", "863", "971", "1151", "2591", "4373", "6143", "6911", "8191", "8747", "13121", "15551", "23327", "27647", "62207", "73727", "131071", "139967", "165887", "294911", "314927", "442367", "472391", "497663", "524287", "786431", "995327" ]
[ "nonn", "changed" ]
89
1
1
[ "A000040", "A000668", "A003586", "A005105", "A005108", "A005109", "A019434", "A069353", "A069356", "A129469" ]
[ "M0665" ]
N. J. A. Sloane, Simon Plouffe
2025-04-20T20:13:23
oeisdata/seq/A005/A005105.seq
6c223c6d01dfd049e97633d51faa06ae
A005106
Class 2+ primes (for definition see A005105).
[ "13", "19", "29", "41", "43", "59", "61", "67", "79", "83", "89", "97", "101", "109", "131", "137", "139", "149", "167", "179", "197", "199", "211", "223", "229", "239", "241", "251", "263", "269", "271", "281", "283", "293", "307", "317", "349", "359", "367", "373", "419", "433", "439", "449", "461", "479", "499", "503", "509", "557", "563", "577", "587", "593" ]
[ "nonn" ]
21
1
1
[ "A005105", "A005106", "A005107", "A005108", "A005113" ]
[ "M4889" ]
N. J. A. Sloane, Simon Plouffe
2024-03-26T07:38:21
oeisdata/seq/A005/A005106.seq
d11b69fba3963697f36cb1ad9bb529a5
A005107
Class 3+ primes (for definition see A005105).
[ "37", "103", "113", "151", "157", "163", "173", "181", "193", "227", "233", "257", "277", "311", "331", "337", "347", "353", "379", "389", "397", "401", "409", "421", "457", "463", "467", "487", "491", "521", "523", "541", "547", "569", "571", "601", "607", "613", "631", "653", "683", "701", "727", "733", "773", "787", "797", "811", "821", "829", "853", "857" ]
[ "nonn" ]
19
1
1
[ "A005105", "A005106", "A005107", "A005108", "A005113" ]
[ "M5261" ]
N. J. A. Sloane, Simon Plouffe
2014-01-13T11:57:34
oeisdata/seq/A005/A005107.seq
1974e610f08f0c357e25d81e4e8f2312
A005108
Class 4+ primes (for definition see A005105).
[ "73", "313", "443", "617", "661", "673", "677", "691", "739", "757", "823", "887", "907", "941", "977", "1093", "1109", "1129", "1201", "1213", "1303", "1361", "1447", "1453", "1543", "1553", "1621", "1627", "1657", "1753", "1811", "1867", "1873", "1993", "1997", "2017", "2081", "2083", "2113", "2269", "2273", "2281", "2293", "2333", "2341" ]
[ "nonn" ]
22
1
1
[ "A005105", "A005106", "A005107", "A005108", "A005113" ]
[ "M5350" ]
N. J. A. Sloane, Simon Plouffe
2014-01-13T11:56:19
oeisdata/seq/A005/A005108.seq
27180db62689d18150116f17dc93faa9
A005109
Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1.
[ "2", "3", "5", "7", "13", "17", "19", "37", "73", "97", "109", "163", "193", "257", "433", "487", "577", "769", "1153", "1297", "1459", "2593", "2917", "3457", "3889", "10369", "12289", "17497", "18433", "39367", "52489", "65537", "139969", "147457", "209953", "331777", "472393", "629857", "746497", "786433", "839809", "995329", "1179649", "1492993", "1769473", "1990657" ]
[ "nonn", "nice", "easy" ]
138
1
1
[ "A000040", "A000668", "A003586", "A005109", "A019434", "A048135", "A048136", "A056637", "A077497", "A077498", "A077500", "A081426", "A122259", "A374577", "A374578" ]
[ "M0673" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005109.seq
df74d0857ba72e212ba4df405f89caf6
A005110
Class 2- primes (for definition see A005109).
[ "11", "29", "31", "41", "43", "53", "61", "71", "79", "101", "103", "113", "127", "131", "137", "149", "151", "157", "181", "191", "197", "211", "223", "229", "239", "241", "251", "271", "281", "293", "307", "313", "337", "379", "389", "401", "409", "421", "439", "443", "449", "457", "491", "521", "541", "547", "571", "593", "601", "613", "631", "641", "647", "653", "673" ]
[ "nonn" ]
22
1
1
[ "A005109", "A005110", "A005111", "A005112", "A005113", "A056637", "A081424", "A081425", "A081426", "A081427", "A081428", "A081429", "A081430" ]
[ "M4783" ]
N. J. A. Sloane, Simon Plouffe
2015-03-15T18:51:44
oeisdata/seq/A005/A005110.seq
e39ff7e35faf7f123b6e2ccfe7d020d5
A005111
Class 3- primes (for definition see A005109).
[ "23", "59", "67", "83", "89", "107", "173", "199", "227", "233", "263", "311", "317", "331", "349", "353", "367", "373", "383", "397", "419", "431", "463", "479", "503", "509", "523", "563", "569", "587", "607", "617", "619", "661", "683", "727", "733", "739", "743", "787", "809", "821", "823", "853", "859", "881", "887", "907", "929", "947", "977", "983", "991", "1031", "1033" ]
[ "nonn" ]
18
1
1
[ "A005109", "A005110", "A005111", "A005112", "A005113", "A056637", "A081424", "A081425", "A081426", "A081427", "A081428", "A081429", "A081430" ]
[ "M5133" ]
N. J. A. Sloane, Simon Plouffe
2012-09-22T11:09:59
oeisdata/seq/A005/A005111.seq
4ab7e730c75c030263bbd88022299219
A005112
Class 4- primes (for definition see A005109).
[ "47", "139", "167", "179", "269", "277", "347", "461", "467", "499", "599", "643", "691", "709", "797", "827", "829", "839", "857", "863", "967", "997", "1013", "1019", "1039", "1063", "1069", "1151", "1163", "1181", "1289", "1367", "1381", "1399", "1427", "1487", "1493", "1499", "1579", "1609", "1619", "1657", "1867", "1877", "1889", "1933", "1979" ]
[ "nonn" ]
18
1
1
[ "A005109", "A005110", "A005111", "A005112", "A005113", "A056637", "A081424", "A081425", "A081426", "A081427", "A081428", "A081429", "A081430" ]
[ "M5289" ]
N. J. A. Sloane, Simon Plouffe
2012-09-22T11:10:27
oeisdata/seq/A005/A005112.seq
3e058f88f4c8b53ef0fb980f686900dc
A005113
Smallest prime in class n (sometimes written n+) according to the Erdős-Selfridge classification of primes.
[ "2", "13", "37", "73", "1021", "2917", "15013", "49681", "532801", "1065601", "8524807", "68198461", "545587687", "1704961513", "23869461181", "288310406533" ]
[ "more", "nonn" ]
44
1
1
[ "A005105", "A005106", "A005107", "A005108", "A005113", "A019268", "A056637", "A081633", "A081639", "A084071", "A090468", "A129469", "A129474", "A129475" ]
[ "M2057" ]
N. J. A. Sloane
2018-07-07T06:14:11
oeisdata/seq/A005/A005113.seq
e39f90930702970b40f6137370377e69
A005114
Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function (A001065).
[ "2", "5", "52", "88", "96", "120", "124", "146", "162", "188", "206", "210", "216", "238", "246", "248", "262", "268", "276", "288", "290", "292", "304", "306", "322", "324", "326", "336", "342", "372", "406", "408", "426", "430", "448", "472", "474", "498", "516", "518", "520", "530", "540", "552", "556", "562", "576", "584", "612", "624", "626", "628", "658" ]
[ "nonn", "nice" ]
120
1
1
[ "A001065", "A005114", "A048138", "A057709", "A064000", "A078923", "A152454", "A231964", "A283152", "A284147" ]
[ "M1552" ]
N. J. A. Sloane
2025-03-14T10:51:12
oeisdata/seq/A005/A005114.seq
675d70b6af8319f4e469aaddcfd8921d
A005115
Let i, i+d, i+2d, ..., i+(n-1)d be an n-term arithmetic progression of primes; choose the one which minimizes the last term; then a(n) = last term i+(n-1)d.
[ "2", "3", "7", "23", "29", "157", "907", "1669", "1879", "2089", "249037", "262897", "725663", "36850999", "173471351", "198793279", "4827507229", "17010526363", "83547839407", "572945039351", "6269243827111" ]
[ "nonn", "hard", "more", "nice" ]
50
1
1
[ "A005115", "A006560", "A088430", "A093364", "A096003", "A113827", "A113830", "A113834", "A133277" ]
[ "M0854" ]
N. J. A. Sloane
2021-12-26T21:03:01
oeisdata/seq/A005/A005115.seq
9b05ee2f0e149ce60335caabf5046cc3
A005116
Number of protruded partitions of n with largest part at most 10.
[ "1", "3", "6", "13", "25", "50", "94", "178", "328", "601", "1083", "1940", "3436", "6047", "10558", "18326", "31614", "54265", "92683", "157626", "266985", "450580", "757851", "1270757", "2124721", "3543318", "5894831", "9785243", "16210036", "26802756", "44240560", "72906608", "119969779" ]
[ "nonn" ]
22
1
2
null
[ "M2571" ]
N. J. A. Sloane and Richard Stanley
2025-01-05T19:51:33
oeisdata/seq/A005/A005116.seq
6e5e482027317105d892d94e13e8ca8e
A005117
Squarefree numbers: numbers that are not divisible by a square greater than 1.
[ "1", "2", "3", "5", "6", "7", "10", "11", "13", "14", "15", "17", "19", "21", "22", "23", "26", "29", "30", "31", "33", "34", "35", "37", "38", "39", "41", "42", "43", "46", "47", "51", "53", "55", "57", "58", "59", "61", "62", "65", "66", "67", "69", "70", "71", "73", "74", "77", "78", "79", "82", "83", "85", "86", "87", "89", "91", "93", "94", "95", "97", "101", "102", "103", "105", "106", "107", "109", "110", "111", "113" ]
[ "nonn", "easy", "nice", "core", "changed" ]
527
1
2
[ "A000040", "A000688", "A001414", "A002110", "A003277", "A005117", "A008472", "A008683", "A008966", "A013928", "A013929", "A020753", "A020754", "A020755", "A027750", "A030059", "A030229", "A033197", "A034444", "A039956", "A046660", "A048672", "A053797", "A056911", "A057918", "A059956", "A071403", "A072284", "A072774", "A076259", "A077610", "A120992", "A133466", "A136742", "A136743", "A160764", "A173143", "A206778", "A209061", "A215366", "A235488", "A243289", "A243347", "A243348", "A243351", "A261034", "A265668", "A265675", "A274546", "A276378" ]
[ "M0617" ]
N. J. A. Sloane
2025-04-22T00:15:46
oeisdata/seq/A005/A005117.seq
24d7a0fd5bf028609ae30a85d3608084
A005118
Number of simple allowable sequences on 1..n containing the permutation 12...n.
[ "1", "1", "1", "2", "16", "768", "292864", "1100742656", "48608795688960", "29258366996258488320", "273035280663535522487992320", "44261486084874072183645699204710400", "138018895500079485095943559213817088756940800" ]
[ "nonn", "easy", "nice" ]
100
0
4
[ "A003121", "A005118", "A018241", "A057863", "A246865", "A289778" ]
[ "M2097" ]
N. J. A. Sloane
2024-11-11T22:29:47
oeisdata/seq/A005/A005118.seq
454177ec6c6d908999f4cff7c0f02881
A005119
Infinitesimal generator of x*(x + 1).
[ "1", "1", "3", "16", "124", "1256", "15576", "226248", "3729216", "68179968", "1361836800", "29501349120", "693638208000", "17815908096000", "502048890201600", "15388268595840000", "500579319427891200", "16817771937344716800", "581609175119297740800" ]
[ "sign", "nice" ]
40
1
3
[ "A005119", "A030528" ]
[ "M3024" ]
N. J. A. Sloane, Simon Plouffe
2025-02-03T11:54:24
oeisdata/seq/A005/A005119.seq
561904c01a5a8842a7bcc3d90e7021cd
A005120
A sixth-order linear divisibility sequence: a(n+6) = -3*a(n+5) - 5*a(n+4) - 5*a(n+3) - 5*a(n+2) - 3*a(n+1) - a(n).
[ "0", "1", "-1", "1", "-1", "-1", "5", "-8", "7", "1", "-19", "43", "-55", "27", "64", "-211", "343", "-307", "-85", "911", "-1919", "2344", "-989", "-3151", "9625", "-15049", "12609", "5671", "-42496", "85609", "-100225", "33977", "154007", "-437009", "657901", "-513512", "-335665", "1974097", "-3808891", "4265379" ]
[ "sign", "easy" ]
44
0
7
[ "A001608", "A005120" ]
[ "M3770" ]
N. J. A. Sloane
2023-10-26T22:41:54
oeisdata/seq/A005/A005120.seq
e72e4c08e025b8f14222c1ad1a9f860f
A005121
Number of ultradissimilarity relations on an n-set.
[ "1", "1", "4", "32", "436", "9012", "262760", "10270696", "518277560", "32795928016", "2542945605432", "237106822506952", "26173354092593696", "3375693096567983232", "502995942483693043200", "85750135569136650473360", "16583651916595710735271248", "3611157196483089769387182064", "879518067472225603327860638128" ]
[ "nonn", "nice", "easy" ]
67
1
3
[ "A000110", "A000258", "A002846", "A005121", "A006472", "A006541", "A008826", "A213427", "A265947", "A317145" ]
[ "M3649" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005121.seq
2ada9d2d25f14036d4eef482a46a55c1
A005122
Numbers k such that 8k - 1 is prime.
[ "1", "3", "4", "6", "9", "10", "13", "16", "19", "21", "24", "25", "28", "30", "33", "34", "39", "45", "46", "48", "54", "55", "58", "60", "61", "63", "75", "76", "79", "81", "90", "91", "93", "94", "103", "105", "108", "111", "114", "115", "121", "123", "124", "129", "130", "133", "136", "138", "144", "153", "154", "160", "163", "165", "166", "171", "175", "178", "180" ]
[ "nonn", "easy" ]
38
1
2
[ "A005122", "A007522" ]
null
N. J. A. Sloane
2024-02-05T00:54:38
oeisdata/seq/A005/A005122.seq
58a15f4bb08a39326613ed273484d55f
A005123
Numbers k such that 8k + 1 is prime.
[ "2", "5", "9", "11", "12", "14", "17", "24", "29", "30", "32", "35", "39", "42", "44", "50", "51", "54", "56", "57", "65", "71", "72", "74", "75", "77", "80", "84", "95", "96", "101", "107", "110", "116", "117", "119", "122", "126", "129", "131", "137", "141", "144", "149", "150", "152", "156", "161", "162", "165", "170", "176", "179", "185", "186", "194", "200", "201" ]
[ "nonn" ]
35
1
1
[ "A005123", "A007519", "A111174", "A115249" ]
null
N. J. A. Sloane
2024-02-05T00:54:55
oeisdata/seq/A005/A005123.seq
ef350fc539ea16f6d46cd4def72cfb71
A005124
Numbers k such that 8k + 3 is prime.
[ "0", "1", "2", "5", "7", "8", "10", "13", "16", "17", "20", "22", "26", "28", "31", "35", "38", "41", "43", "47", "52", "55", "58", "61", "62", "65", "68", "70", "71", "73", "77", "80", "82", "85", "86", "92", "98", "101", "103", "107", "110", "113", "118", "121", "127", "131", "136", "140", "145", "146", "148", "157", "160", "161", "163", "178", "181", "182", "185", "187" ]
[ "nonn" ]
29
1
3
null
null
N. J. A. Sloane
2024-02-05T00:55:17
oeisdata/seq/A005/A005124.seq
edd66004a73a8ea9c32c45b5d560cdcb
A005125
Numbers k such that 8k - 3 is prime.
[ "1", "2", "4", "5", "7", "8", "13", "14", "19", "20", "22", "23", "25", "29", "34", "35", "37", "40", "44", "47", "49", "50", "53", "58", "64", "68", "70", "77", "82", "83", "85", "88", "89", "92", "95", "97", "100", "103", "104", "107", "110", "118", "125", "127", "128", "133", "134", "137", "139", "140", "148", "152" ]
[ "nonn", "easy" ]
23
1
2
null
null
N. J. A. Sloane
2024-02-05T00:55:27
oeisdata/seq/A005/A005125.seq
6c495f4133fe18ff930bec88804be018
A005126
a(n) = 2^n + n + 1.
[ "2", "4", "7", "12", "21", "38", "71", "136", "265", "522", "1035", "2060", "4109", "8206", "16399", "32784", "65553", "131090", "262163", "524308", "1048597", "2097174", "4194327", "8388632", "16777241", "33554458", "67108891", "134217756", "268435485", "536870942", "1073741855", "2147483680", "4294967329", "8589934626" ]
[ "nonn", "easy" ]
60
0
1
[ "A005126", "A128715", "A194455" ]
[ "M1061" ]
Colin Mallows
2022-09-08T08:44:33
oeisdata/seq/A005/A005126.seq
02ce7aa5e6aefe6ff33d761998b36b7a
A005127
Number of k for which n does not divide Stirling cycle numbers [ {n \atop k} ].
[ "1", "0", "2", "2", "4", "2", "5", "2", "6", "4", "5", "2", "9", "2", "9", "7", "8", "2", "9", "2", "12", "7", "9", "2", "13", "6", "9", "10", "18", "2", "19", "2", "12", "8", "5", "10", "16", "2", "9", "10", "18", "2", "20", "2", "22", "17", "17", "2", "19", "8", "15", "19", "23", "2", "27", "9", "25", "7", "17", "2", "37", "2", "33", "16", "20", "14", "20", "2", "12", "19", "26", "2", "28", "2", "9", "25", "22", "16", "37", "2", "26", "28", "9", "2" ]
[ "nonn" ]
17
0
3
null
null
Olivier Gérard
2012-10-28T05:24:08
oeisdata/seq/A005/A005127.seq
3c6238ba2d5cf3f3d05da4a2e339ea93
A005128
Number of k for which n does not divide Stirling_2 subset numbers S(n, k).
[ "1", "0", "2", "2", "4", "2", "5", "2", "8", "7", "7", "2", "10", "2", "9", "10", "16", "2", "16", "2", "16", "11", "13", "2", "20", "15", "13", "22", "20", "2", "13", "2", "32", "14", "11", "20", "32", "2", "18", "18", "33", "2", "33", "2", "26", "31", "20", "2", "44", "28", "34", "20", "31", "2", "47", "23", "38", "19", "18", "2", "42", "2", "15", "37", "64", "29", "37", "2", "33", "22", "43", "2", "58", "2", "26", "57", "40", "42" ]
[ "nonn" ]
15
0
3
[ "A005128", "A048993" ]
null
Olivier Gérard
2012-10-27T23:06:03
oeisdata/seq/A005/A005128.seq
b2333147c4811c18f28d1a1b2743ecdc
A005129
Theta series of {E_6}* lattice.
[ "1", "0", "54", "72", "0", "432", "270", "0", "918", "720", "0", "2160", "936", "0", "2700", "2160", "0", "5184", "2214", "0", "5616", "3600", "0", "9504", "4590", "0", "9180", "6552", "0", "15120", "5184", "0", "14742", "10800", "0", "21600", "9360", "0", "19548", "12240", "0", "30240", "13500", "0", "28080", "17712", "0", "39744", "14760", "0", "32454" ]
[ "nonn", "nice", "easy" ]
33
0
3
[ "A004007", "A005129" ]
[ "M5309" ]
N. J. A. Sloane
2022-09-08T08:44:33
oeisdata/seq/A005/A005129.seq
b445b8734c5cf166dbb23ec860baa358
A005130
Robbins numbers: a(n) = Product_{k=0..n-1} (3k+1)!/(n+k)!; also the number of descending plane partitions whose parts do not exceed n; also the number of n X n alternating sign matrices (ASM's).
[ "1", "1", "2", "7", "42", "429", "7436", "218348", "10850216", "911835460", "129534272700", "31095744852375", "12611311859677500", "8639383518297652500", "9995541355448167482000", "19529076234661277104897200", "64427185703425689356896743840", "358869201916137601447486156417296" ]
[ "nonn", "easy", "nice", "core" ]
230
0
3
[ "A003827", "A005130", "A005156", "A005158", "A005160", "A005164", "A006366", "A048601", "A049503", "A050204", "A194827", "A227833" ]
[ "M1808" ]
N. J. A. Sloane
2025-02-19T12:06:50
oeisdata/seq/A005/A005130.seq
e8c998509b0074299e339142c151d75d
A005131
A generalized continued fraction for Euler's number e.
[ "1", "0", "1", "1", "2", "1", "1", "4", "1", "1", "6", "1", "1", "8", "1", "1", "10", "1", "1", "12", "1", "1", "14", "1", "1", "16", "1", "1", "18", "1", "1", "20", "1", "1", "22", "1", "1", "24", "1", "1", "26", "1", "1", "28", "1", "1", "30", "1", "1", "32", "1", "1", "34", "1", "1", "36", "1", "1", "38", "1", "1", "40", "1", "1", "42" ]
[ "nonn", "cofr" ]
47
0
5
[ "A003417", "A005131", "A100261" ]
null
Russ Cox
2018-02-21T03:30:14
oeisdata/seq/A005/A005131.seq
1a2d64aff781585d241fa2b69d8d08c9
A005132
Recamán's sequence (or Recaman's sequence): a(0) = 0; for n > 0, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n.
[ "0", "1", "3", "6", "2", "7", "13", "20", "12", "21", "11", "22", "10", "23", "9", "24", "8", "25", "43", "62", "42", "63", "41", "18", "42", "17", "43", "16", "44", "15", "45", "14", "46", "79", "113", "78", "114", "77", "39", "78", "38", "79", "37", "80", "36", "81", "35", "82", "34", "83", "33", "84", "32", "85", "31", "86", "30", "87", "29", "88", "28", "89", "27", "90", "26", "91", "157", "224", "156", "225", "155" ]
[ "nonn", "nice", "hear", "look" ]
370
0
3
[ "A005132", "A008336", "A046901", "A057165", "A057166", "A057167", "A063733", "A064227", "A064228", "A064284", "A064288", "A064289", "A064290", "A064291", "A064387", "A064388", "A064389", "A065056", "A066201", "A079053", "A119632", "A160356", "A171884", "A228474", "A324784", "A324785", "A324786", "A330791", "A331659", "A331670" ]
[ "M2511" ]
N. J. A. Sloane and Simon Plouffe, May 16 1991
2025-01-20T22:54:50
oeisdata/seq/A005/A005132.seq
ff7c903f892c6a6943c889916a954793
A005133
Number of index n subgroups of modular group PSL_2(Z).
[ "1", "1", "4", "8", "5", "22", "42", "40", "120", "265", "286", "764", "1729", "2198", "5168", "12144", "17034", "37702", "88958", "136584", "288270", "682572", "1118996", "2306464", "5428800", "9409517", "19103988", "44701696", "80904113", "163344502", "379249288", "711598944", "1434840718", "3308997062", "6391673638", "12921383032", "29611074174", "58602591708", "119001063028", "271331133136", "547872065136", "1119204224666", "2541384297716", "5219606253184", "10733985041978", "24300914061436", "50635071045768", "104875736986272", "236934212877684", "499877970985660" ]
[ "nonn", "nice", "easy" ]
52
1
3
[ "A005133", "A121357" ]
[ "M3320" ]
Simon Plouffe
2022-02-26T11:49:34
oeisdata/seq/A005/A005133.seq
7abfcdb45e51b0a808b04c5009dd25d0
A005134
Number of n-dimensional unimodular lattices (or quadratic forms).
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "3", "3", "4", "5", "8", "9", "13", "16", "28", "40", "68", "117", "297", "665", "2566", "17059", "374062" ]
[ "nonn", "nice", "hard" ]
24
0
9
[ "A005134", "A054907", "A054908", "A054909", "A054911" ]
[ "M0219" ]
N. J. A. Sloane
2025-02-10T02:08:00
oeisdata/seq/A005/A005134.seq
d2371ab2d2d6800e51bc31d3aedc383d
A005135
Number of laminated lattices of dimension n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "23" ]
[ "nonn", "more" ]
27
0
12
null
[ "M0431" ]
N. J. A. Sloane
2023-10-26T23:16:14
oeisdata/seq/A005/A005135.seq
ced37999f76c4fc68290b97f96bb7f4e
A005136
Highest minimal norm of n-dimensional unimodular lattice.
[ "0", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "4", "2", "3", "3", "3", "3", "3", "3", "4", "3" ]
[ "nonn", "hard" ]
13
0
9
null
[ "M0057" ]
N. J. A. Sloane
2023-10-26T23:16:18
oeisdata/seq/A005/A005136.seq
d5c489ac187d948dc5c7232258315d6a
A005137
Highest minimal distance of self-dual code of length 2n.
[ "0", "2", "2", "2", "4", "2", "4", "4", "4", "4", "4", "6", "8", "6", "6", "6", "8", "6", "8", "8", "8", "8", "8", "10", "12", "10", "10", "10", "12", "10", "12" ]
[ "nonn", "hard" ]
11
0
2
null
[ "M0233" ]
N. J. A. Sloane
2023-10-26T22:51:29
oeisdata/seq/A005/A005137.seq
ae832daff65517791844f8379c87594e
A005138
Number of n-dimensional determinant 2 lattices.
[ "0", "1", "1", "1", "1", "1", "1", "2", "2", "3", "3", "4", "4", "6", "7", "11", "14", "24", "30" ]
[ "nonn" ]
11
0
8
null
[ "M0262" ]
N. J. A. Sloane
2023-10-26T22:45:45
oeisdata/seq/A005/A005138.seq
e89965618e9257b75172410dd0641688
A005139
Number of n-dimensional determinant 3 lattices.
[ "0", "1", "2", "2", "2", "2", "3", "3", "4", "5", "7", "8", "10", "13", "19", "24", "36", "53" ]
[ "nonn" ]
12
0
3
null
[ "M0218" ]
N. J. A. Sloane
2023-10-26T22:46:06
oeisdata/seq/A005/A005139.seq
77abea6142904426494d9eaecc16a978
A005140
Number of n-dimensional determinant 4 lattices.
[ "0", "1", "1", "2", "3", "4", "5", "6", "7", "10", "13", "16", "22" ]
[ "nonn" ]
11
0
4
null
[ "M0499" ]
N. J. A. Sloane
2023-10-26T22:46:29
oeisdata/seq/A005/A005140.seq
189efab0e8d84313add6acf4fe1aac8c
A005141
Number of genera of forms with |determinant| = n.
[ "2", "2", "4", "9", "4", "4", "4", "10", "8", "4", "4" ]
[ "nonn", "nice", "more" ]
18
1
1
null
[ "M0333" ]
N. J. A. Sloane
2021-05-18T23:41:58
oeisdata/seq/A005/A005141.seq
ea56b123bae8ef2e396500e351826922
A005142
Number of connected bipartite graphs with n nodes.
[ "1", "1", "1", "1", "3", "5", "17", "44", "182", "730", "4032", "25598", "212780", "2241730", "31193324", "575252112", "14218209962", "472740425319", "21208887576786", "1286099113807999", "105567921675718772", "11743905783670560579", "1772771666309380358809", "363526952035325887859823", "101386021137641794979558045" ]
[ "nonn", "nice" ]
54
0
5
[ "A005142", "A033995", "A116079", "A318869", "A318870" ]
[ "M2501" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005142.seq
2a70b2986104a887ad7c2a2221b07d70
A005143
Number of sub-Eulerian graphs with n nodes.
[ "1", "1", "3", "10", "45", "274" ]
[ "nonn", "more" ]
12
2
3
null
[ "M2869" ]
N. J. A. Sloane
2023-10-26T22:48:52
oeisdata/seq/A005/A005143.seq
1e3d3f8a7312915fb5509c7bc016c47e
A005144
Number of sub-Hamiltonian graphs with n nodes.
[ "1", "1", "2", "10", "43", "346" ]
[ "nonn", "more" ]
13
2
3
null
[ "M1968" ]
N. J. A. Sloane
2023-10-26T22:49:09
oeisdata/seq/A005/A005144.seq
1f09570f2208c8a90e0c64581cc1e264
A005145
n copies of n-th prime.
[ "2", "3", "3", "5", "5", "5", "7", "7", "7", "7", "11", "11", "11", "11", "11", "13", "13", "13", "13", "13", "13", "17", "17", "17", "17", "17", "17", "17", "19", "19", "19", "19", "19", "19", "19", "19", "23", "23", "23", "23", "23", "23", "23", "23", "23", "29", "29", "29", "29", "29", "29", "29", "29", "29", "29", "31", "31", "31", "31", "31", "31", "31", "31", "31", "31", "31" ]
[ "nonn", "nice", "tabl" ]
71
1
1
[ "A000040", "A002024", "A003961", "A005145", "A031368", "A033286", "A097906", "A175944", "A297845", "A306697", "A329329" ]
null
Russ Cox
2024-02-29T19:10:12
oeisdata/seq/A005/A005145.seq
9d5b7449ce587e723f66b02c1c1b461d
A005146
Numerators of numbers occurring in continued fraction connected with expansion of gamma function.
[ "1", "1", "53", "195", "22999", "29944523", "109535241009", "29404527905795295658", "455377030420113432210116914702", "26370812569397719001931992945645578779849", "152537496709054809881638897472985990866753853122697839", "100043420063777451042472529806266909090824649341814868347109676190691" ]
[ "nonn", "frac", "nice" ]
33
0
3
[ "A005146", "A005147" ]
[ "M5308" ]
Simon Plouffe and N. J. A. Sloane
2018-05-08T15:11:54
oeisdata/seq/A005/A005146.seq
2b9b033e7cf4884a51f35fd9b97093b3
A005147
Denominators of numbers occurring in continued fraction connected with expansion of gamma function.
[ "12", "30", "210", "371", "22737", "19733142", "48264275462", "9769214287853155785", "113084128923675014537885725485", "5271244267917980801966553649147604697542", "24274291553105128438297398108902195365373879212227726", "13346384670164266280033479022693768890138348905413621178450736182873" ]
[ "nonn", "frac", "nice" ]
32
0
1
[ "A005146", "A005147" ]
[ "M4831" ]
Simon Plouffe and N. J. A. Sloane
2018-05-08T15:11:54
oeisdata/seq/A005/A005147.seq
522266621772f891d68e8182cc6f1a26
A005148
Sequence of coefficients arising in connection with a rapidly converging series for Pi.
[ "0", "1", "47", "2488", "138799", "7976456", "467232200", "27736348480", "1662803271215", "100442427373480", "6103747246289272", "372725876150863808", "22852464771010647496", "1405886026610765892544", "86741060172969340021952" ]
[ "nonn", "easy", "nice" ]
80
0
3
[ "A005148", "A005149", "A018900", "A060236", "A076657" ]
[ "M5290" ]
Simon Plouffe and N. J. A. Sloane
2023-08-02T18:57:05
oeisdata/seq/A005/A005148.seq
c05b13cadf369085a99601009fbcd8ff
A005149
Sequence of coefficients arising in connection with a rapidly converging series for Pi.
[ "1", "-24", "852", "-35744", "1645794", "-80415216", "4094489992", "-214888573248", "11542515402255", "-631467591949480", "35063515239394764", "-1971043639046131296", "111949770626330347638", "-6414671157989386260432", "370360217892318010055832", "-21525284426246779936288192" ]
[ "sign", "nice" ]
40
1
2
[ "A005148", "A005149", "A014103", "A195130" ]
[ "M5168" ]
Simon Plouffe and N. J. A. Sloane
2022-01-31T01:32:07
oeisdata/seq/A005/A005149.seq
a941744068885e5a46b7e0dcd1ea1d94
A005150
Look and Say sequence: describe the previous term! (method A - initial term is 1).
[ "1", "11", "21", "1211", "111221", "312211", "13112221", "1113213211", "31131211131221", "13211311123113112211", "11131221133112132113212221", "3113112221232112111312211312113211", "1321132132111213122112311311222113111221131221", "11131221131211131231121113112221121321132132211331222113112211", "311311222113111231131112132112311321322112111312211312111322212311322113212221" ]
[ "nonn", "base", "easy", "nice" ]
280
1
2
[ "A001140", "A001141", "A001143", "A001145", "A001151", "A001154", "A001155", "A001387", "A001637", "A004977", "A005150", "A005341", "A006715", "A006751", "A007651", "A014715", "A022466", "A022467", "A022468", "A060857", "A079562", "A098097", "A100108", "A119566", "A221646", "A225212", "A225224", "A253677", "A334132" ]
[ "M4780" ]
N. J. A. Sloane
2025-03-16T10:44:24
oeisdata/seq/A005/A005150.seq
3e37283cafa326d6890468aba3f38260
A005151
Summarize the previous term (digits in increasing order), starting with a(1) = 1.
[ "1", "11", "21", "1112", "3112", "211213", "312213", "212223", "114213", "31121314", "41122314", "31221324", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314", "21322314" ]
[ "nonn", "base", "easy" ]
87
1
2
[ "A005150", "A005151", "A023989", "A047842", "A060857", "A083671", "A118628" ]
[ "M4779" ]
N. J. A. Sloane
2024-02-08T07:10:44
oeisdata/seq/A005/A005151.seq
09e841a18cc628c566837f56c7b71419
A005152
Rotation distance between binary trees on n nodes.
[ "0", "1", "2", "4", "5", "7", "9", "11", "12", "15", "16", "18", "20", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "42", "44", "46", "48", "50", "52", "54", "56", "58", "60", "62", "64", "66", "68", "70", "72", "74", "76", "78", "80", "82", "84", "86", "88", "90", "92", "94", "96", "98", "100" ]
[ "nonn", "nice" ]
54
1
3
null
[ "M0963" ]
N. J. A. Sloane
2023-06-26T14:34:06
oeisdata/seq/A005/A005152.seq
38fb984cded643d52a6652925d713b8d
A005153
Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers.
[ "1", "2", "4", "6", "8", "12", "16", "18", "20", "24", "28", "30", "32", "36", "40", "42", "48", "54", "56", "60", "64", "66", "72", "78", "80", "84", "88", "90", "96", "100", "104", "108", "112", "120", "126", "128", "132", "140", "144", "150", "156", "160", "162", "168", "176", "180", "192", "196", "198", "200", "204", "208", "210", "216", "220", "224", "228", "234", "240", "252" ]
[ "nonn", "nice", "easy" ]
279
1
2
[ "A002093", "A005153", "A007620", "A027750", "A030057", "A033630", "A103288", "A119348", "A174533", "A174973" ]
[ "M0991" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005153.seq
23f82c813da5a1aae52194710dff59a3
A005154
a(0) = 1, a(1) = 2; thereafter a(n) = 3*a(n-1)^2 - 2*a(n-2)^4.
[ "1", "2", "10", "268", "195472", "104310534400", "29722161121961969778688", "2413441860555924454205324333893477339897004032", "15913289476042091181119569948276231488639535067163704670852319029791565485433738366445158400" ]
[ "nonn", "easy" ]
50
0
2
[ "A005154", "A076725" ]
[ "M1992" ]
N. J. A. Sloane
2023-10-27T08:21:07
oeisdata/seq/A005/A005154.seq
0a4c90534ab2711a7cea0b923ac814fc
A005155
Number of degree sequences of n-node graphs.
[ "1", "1", "2", "8", "54", "533", "6944", "111850", "2135740", "47003045", "1168832808", "32363244260", "986532609608", "32810811179569", "1181865951824800", "45823912079507918", "1902469319507438352", "84195282530581058825", "3956365033583165905568", "196716723188140236180160" ]
[ "nonn", "nice", "easy" ]
57
0
3
[ "A004251", "A005155" ]
[ "M1886" ]
N. J. A. Sloane
2023-10-27T22:07:51
oeisdata/seq/A005/A005155.seq
80d01859469f822cd63b992840e407a7
A005156
Number of alternating sign 2n+1 X 2n+1 matrices symmetric about the vertical axis (VSASM's); also 2n X 2n off-diagonally symmetric alternating sign matrices (OSASM's).
[ "1", "1", "3", "26", "646", "45885", "9304650", "5382618660", "8878734657276", "41748486581283118", "559463042542694360707", "21363742267675013243931852", "2324392978926652820310084179576", "720494439459132215692530771292602232", "636225819409712640497085074811372777428304" ]
[ "nonn", "nice", "easy" ]
59
0
3
[ "A005156", "A109074", "A134357" ]
[ "M3115" ]
N. J. A. Sloane
2025-02-19T12:06:25
oeisdata/seq/A005/A005156.seq
726e0a73c238b40bd09c48ec35ceecdb
A005157
Number of totally symmetric plane partitions that fit in an n X n X n box.
[ "1", "2", "5", "16", "66", "352", "2431", "21760", "252586", "3803648", "74327145", "1885102080", "62062015500", "2652584509440", "147198472495020", "10606175914819584", "992340657705109416", "120567366227960791040", "19023173201224270401428", "3897937005297330777227264" ]
[ "nonn", "nice", "easy", "changed" ]
103
0
2
[ "A005157", "A049505", "A184173", "A214564", "A323848" ]
[ "M1499" ]
N. J. A. Sloane
2025-04-20T20:13:18
oeisdata/seq/A005/A005157.seq
cc1e096217c6e17ce8c60eb2e3af3421
A005158
Number of alternating sign n X n matrices invariant under a half-turn.
[ "1", "2", "3", "10", "25", "140", "588", "5544", "39204", "622908", "7422987", "198846076" ]
[ "nonn", "nice", "more" ]
53
1
2
[ "A005158", "A059475" ]
[ "M0902" ]
N. J. A. Sloane
2025-01-08T09:29:25
oeisdata/seq/A005/A005158.seq
95c1a80c60ac62421c4d21d9c850e478
A005159
a(n) = 3^n*Catalan(n).
[ "1", "3", "18", "135", "1134", "10206", "96228", "938223", "9382230", "95698746", "991787004", "10413763542", "110546105292", "1184422556700", "12791763612360", "139110429284415", "1522031755700070", "16742349312700770", "185047018719324300", "2054021907784499730" ]
[ "nonn", "easy", "nice", "changed" ]
146
0
2
[ "A000108", "A000244", "A005159", "A025226", "A053764", "A085880", "A102994" ]
null
N. J. A. Sloane, Valery A. Liskovets
2025-04-20T20:13:13
oeisdata/seq/A005/A005159.seq
dfd2c56b4e114d19f54d19b120527c86
A005160
Number of alternating sign n X n matrices invariant under a quarter turn.
[ "1", "0", "1", "2", "3", "0", "12", "40", "100", "0", "1225", "6860", "28812", "0", "1037232", "9779616" ]
[ "nonn", "nice", "more" ]
21
1
4
[ "A005160", "A059476" ]
[ "M0396" ]
N. J. A. Sloane
2023-08-23T10:39:32
oeisdata/seq/A005/A005160.seq
c293659bc0a1facb6b3a5123748e6d1d
A005161
Number of alternating sign 2n+1 X 2n+1 matrices symmetric with respect to both horizontal and vertical axes (VHSASM's).
[ "1", "1", "1", "2", "6", "33", "286", "4420", "109820", "4799134", "340879665", "42235307100", "8564558139000", "3012862604463000", "1742901718473961200", "1742218029490675762080", "2873822682985675809192288", "8167157387273280570395662320", "38402596062535617548517706584760", "310388509293255836481583597538626504" ]
[ "nonn", "nice" ]
47
0
4
[ "A005130", "A005156", "A005161", "A005162", "A005163", "A051255", "A059476" ]
[ "M1700" ]
N. J. A. Sloane
2025-02-19T12:06:18
oeisdata/seq/A005/A005161.seq
5a92553d163a22b21b24a9dac10bae85
A005162
Number of alternating sign n X n matrices symmetric with respect to both diagonals.
[ "1", "2", "3", "8", "15", "52", "126", "568", "1782", "10436", "42471", "323144", "1706562", "16866856", "115640460", "1484714416", "13216815036", "220426128584", "2548124192970" ]
[ "nonn", "nice", "more" ]
32
1
2
null
[ "M0877" ]
N. J. A. Sloane and Simon Plouffe
2023-08-27T19:36:56
oeisdata/seq/A005/A005162.seq
b579efb7043596a5a58671f079dc617d
A005163
Number of alternating sign n X n matrices that are symmetric about a diagonal.
[ "1", "2", "5", "16", "67", "368", "2630", "24376", "293770", "4610624", "94080653", "2492747656", "85827875506", "3842929319936", "223624506056156", "16901839470598576", "1659776507866213636", "211853506422044996288", "35137231473111223912310", "7569998079873075147860464" ]
[ "nonn", "easy", "nice" ]
31
1
2
null
[ "M1500" ]
N. J. A. Sloane and Simon Plouffe
2023-09-22T16:13:35
oeisdata/seq/A005/A005163.seq
8eb63072801c4bcce4b09e2ce46dab55
A005164
Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square.
[ "1", "1", "1", "2", "4", "13", "46", "248", "1516", "13654", "142873", "2156888", "38456356", "974936056", "29540545024", "1259111024288", "64726478396896", "4641989615977216", "404396533544588344", "48825344233129714772", "7202552030561982627472", "1464587581921220811285325", "365627222082497915618219716", "125253905685915522767942493032", "52893528399758443649956432899616" ]
[ "nonn", "nice", "more" ]
41
0
4
[ "A005130", "A005164" ]
[ "M1271" ]
N. J. A. Sloane and Simon Plouffe
2022-09-21T08:53:45
oeisdata/seq/A005/A005164.seq
5dde6acc58d27643bebf987ef0a9a612
A005165
Alternating factorials: n! - (n-1)! + (n-2)! - ... 1!.
[ "0", "1", "1", "5", "19", "101", "619", "4421", "35899", "326981", "3301819", "36614981", "442386619", "5784634181", "81393657019", "1226280710981", "19696509177019", "335990918918981", "6066382786809019", "115578717622022981", "2317323290554617019", "48773618881154822981" ]
[ "nonn", "easy", "nice" ]
126
0
4
[ "A000142", "A001272", "A003422", "A005165", "A071828", "A303697", "A343187", "A359808" ]
[ "M3892" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005165.seq
e67e424fa2edd51838d3c7f9cee1d386
A005166
a(0) = 1; a(n) = (1 + a(0)^3 + ... + a(n-1)^3)/n (not always integral!).
[ "1", "2", "5", "45", "22815", "2375152056927", "2233176271342403475345148513527359103" ]
[ "nonn", "easy", "nice" ]
44
0
2
[ "A003504", "A005166", "A005167", "A108394" ]
[ "M1551" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005166.seq
64a2d13b12b20d8ce737f30cc0ea079e
A005167
a(n+1) = (1 + a(0)^4 + ... + a(n)^4 )/(n+1) (not always integral!).
[ "1", "2", "9", "2193", "5782218987645", "223567225753623833253893162919867828939456664850241" ]
[ "easy", "nonn", "nice" ]
32
0
2
[ "A003504", "A005166", "A005167", "A108394" ]
[ "M1957" ]
N. J. A. Sloane
2023-11-17T19:18:02
oeisdata/seq/A005/A005167.seq
1326c6201739343dc4c42bae04983249
A005168
n-th derivative of x^x at 1, divided by n.
[ "1", "1", "1", "2", "2", "9", "-6", "118", "-568", "4716", "-38160", "358126", "-3662088", "41073096", "-500013528", "6573808200", "-92840971200", "1402148010528", "-22554146644416", "385014881294496", "-6952611764874240", "132427188835260480", "-2653529921603890560", "55802195178451990896" ]
[ "sign", "easy", "nice" ]
50
1
4
[ "A005168", "A005727", "A295027", "A295028" ]
[ "M0380" ]
N. J. A. Sloane, R. K. Guy
2023-10-27T19:38:39
oeisdata/seq/A005/A005168.seq
ba62c6f59fbed8c857b95bdcdc0b243e
A005169
Number of fountains of n coins.
[ "1", "1", "1", "2", "3", "5", "9", "15", "26", "45", "78", "135", "234", "406", "704", "1222", "2120", "3679", "6385", "11081", "19232", "33379", "57933", "100550", "174519", "302903", "525734", "912493", "1583775", "2748893", "4771144", "8281088", "14373165", "24946955", "43299485", "75153286", "130440740", "226401112", "392955956", "682038999", "1183789679", "2054659669", "3566196321", "6189714276" ]
[ "nonn", "easy", "nice" ]
175
0
4
[ "A001524", "A005169", "A047998", "A111317", "A138158", "A143951", "A168396", "A185646", "A192728", "A192729", "A192730", "A226999", "A285903", "A291148" ]
[ "M0708" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005169.seq
2e59aa6be7fe42a649cc70a1d663c020
A005170
Erroneous version of A226999.
[ "1", "0", "1", "1", "2", "3", "5", "8", "13", "21", "35", "55", "93", "149", "248", "403", "670", "1082" ]
[ "dead" ]
24
1
5
null
[ "M0694" ]
null
2017-10-12T18:37:46
oeisdata/seq/A005/A005170.seq
d248d9f521fe1abeb9cc11cff0724b53
A005171
Characteristic function of nonprimes: 0 if n is prime, else 1.
[ "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", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1" ]
[ "nonn", "easy" ]
88
1
1
[ "A005171", "A010051", "A018252", "A023890", "A050374", "A052284", "A157423", "A157424" ]
null
Russ Cox
2025-01-05T19:51:33
oeisdata/seq/A005/A005171.seq
d17c48a72b7b4b6e595033afb6665c48
A005172
Number of labeled rooted trees of subsets of an n-set.
[ "1", "4", "32", "416", "7552", "176128", "5018624", "168968192", "6563282944", "288909131776", "14212910809088", "772776684683264", "46017323176296448", "2978458881388183552", "208198894960190160896", "15631251601179130462208", "1254492810303112820555776", "107174403941451434687463424", "9711022458989438255300083712" ]
[ "nonn", "nice", "easy" ]
107
1
2
[ "A005172", "A005640", "A032188", "A225170" ]
[ "M3648" ]
N. J. A. Sloane
2022-05-30T12:28:36
oeisdata/seq/A005/A005172.seq
2017334e5aca9ed06335967574d4ca95
A005173
Number of rooted trees with 3 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.
[ "0", "1", "12", "61", "240", "841", "2772", "8821", "27480", "84481", "257532", "780781", "2358720", "7108921", "21392292", "64307941", "193185960", "580082161", "1741295052", "5225982301", "15682141200", "47054812201", "141181213812", "423577195861", "1270798696440", "3812530307041", "11437859356572", "34314114940621" ]
[ "nonn", "easy" ]
41
1
3
[ "A003063", "A005173", "A094262" ]
[ "M4844" ]
N. J. A. Sloane
2025-03-28T16:11:13
oeisdata/seq/A005/A005173.seq
5937ceb13ca98839412beeec9eb95d7f
A005174
Number of rooted trees with 4 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.
[ "0", "0", "10", "124", "890", "5060", "25410", "118524", "527530", "2276020", "9613010", "40001324", "164698170", "672961380", "2734531810", "11066546524", "44652164810", "179768037140", "722553165810", "2900661482124", "11634003919450", "46630112719300", "186802788139010", "748058256616124" ]
[ "nonn", "easy" ]
50
1
3
[ "A005174", "A094262" ]
[ "M4738" ]
N. J. A. Sloane
2025-03-28T16:07:10
oeisdata/seq/A005/A005174.seq
dce6f32df824d5cb7a69f27c4d34ed83
A005175
Number of rooted trees with 5 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.
[ "0", "0", "3", "131", "1830", "16990", "127953", "851361", "5231460", "30459980", "170761503", "931484191", "4979773890", "26223530970", "136522672653", "704553794621", "3611494269120", "18415268221960", "93516225653403", "473366777478651", "2390054857197150", "12043393363764950", "60590148885015753" ]
[ "nonn", "easy" ]
49
1
3
[ "A005175", "A094262" ]
[ "M3173" ]
N. J. A. Sloane
2025-03-28T16:07:37
oeisdata/seq/A005/A005175.seq
eb32b754822543d24480c4990515d4dd
A005176
Number of regular graphs with n unlabeled nodes.
[ "1", "1", "2", "2", "4", "3", "8", "6", "22", "26", "176", "546", "19002", "389454", "50314870", "2942198546", "1698517037030", "442786966117636", "649978211591622812", "429712868499646587714", "2886054228478618215888598", "8835589045148342277802657274", "152929279364927228928025482936226", "1207932509391069805495173417972533120", "99162609848561525198669168653641835566774" ]
[ "nonn", "nice", "hard" ]
48
0
3
[ "A000012", "A005176", "A005177", "A005638", "A008483", "A033301", "A051031", "A059841", "A068932", "A165626", "A165627", "A165628", "A180260", "A185314", "A185315", "A185316", "A185317", "A185318", "A185319", "A295193" ]
[ "M0303" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005176.seq
a27b0b7643f50014dd227c9ef046d5ba
A005177
Number of connected regular graphs with n nodes.
[ "1", "1", "1", "1", "2", "2", "5", "4", "17", "22", "167", "539", "18979", "389436", "50314796", "2942198440", "1698517036411", "442786966115560", "649978211591600286", "429712868499646474880", "2886054228478618211088773", "8835589045148342277771518309", "152929279364927228928021274993215", "1207932509391069805495173301992815105", "99162609848561525198669168640159162918815" ]
[ "nonn", "nice", "hard" ]
57
0
5
[ "A002851", "A005176", "A005177", "A006820", "A006821", "A006822", "A014377", "A014378", "A014381", "A014382", "A014384", "A068932", "A068934", "A186724", "A186725", "A186726", "A186727", "A186728", "A186729", "A275420" ]
[ "M0347" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005177.seq
ad34371a7212c6f6ec69d46ea9733a43
A005178
Number of domino tilings of 4 X (n-1) board.
[ "0", "1", "1", "5", "11", "36", "95", "281", "781", "2245", "6336", "18061", "51205", "145601", "413351", "1174500", "3335651", "9475901", "26915305", "76455961", "217172736", "616891945", "1752296281", "4977472781", "14138673395", "40161441636", "114079985111", "324048393905" ]
[ "nonn", "easy", "changed" ]
149
0
4
[ "A003757", "A003775", "A005178", "A028468", "A028469", "A028470", "A033507", "A099390", "A188899", "A250662" ]
[ "M3813" ]
N. J. A. Sloane, David Singmaster, Frans J. Faase
2025-04-20T07:59:26
oeisdata/seq/A005/A005178.seq
5f30156e6cf7fb71a65daec5595da559
A005179
Smallest number with exactly n divisors.
[ "1", "2", "4", "6", "16", "12", "64", "24", "36", "48", "1024", "60", "4096", "192", "144", "120", "65536", "180", "262144", "240", "576", "3072", "4194304", "360", "1296", "12288", "900", "960", "268435456", "720", "1073741824", "840", "9216", "196608", "5184", "1260", "68719476736", "786432", "36864", "1680", "1099511627776", "2880" ]
[ "nonn", "nice", "easy" ]
122
1
2
[ "A000005", "A003586", "A005179", "A007416", "A025487", "A037992", "A050376", "A061799", "A099311", "A099313", "A099316", "A262981", "A262983" ]
[ "M1026" ]
N. J. A. Sloane, David Singmaster
2025-02-16T08:32:28
oeisdata/seq/A005/A005179.seq
65acae6e865f039ee70272881bb6d4c0
A005180
Orders of simple groups.
[ "1", "2", "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "60", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "168", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241" ]
[ "nonn", "nice", "easy" ]
35
1
2
[ "A000001", "A000040", "A001034", "A001228", "A005180" ]
[ "M0651" ]
N. J. A. Sloane, R. K. Guy
2024-06-15T17:58:20
oeisdata/seq/A005/A005180.seq
66e2ebbd3b78efb55d69987a9c6b8482
A005181
a(n) = ceiling(exp((n-1)/2)).
[ "1", "1", "2", "3", "5", "8", "13", "21", "34", "55", "91", "149", "245", "404", "666", "1097", "1809", "2981", "4915", "8104", "13360", "22027", "36316", "59875", "98716", "162755", "268338", "442414", "729417", "1202605", "1982760", "3269018", "5389699", "8886111", "14650720", "24154953", "39824785", "65659970", "108254988", "178482301" ]
[ "nonn" ]
52
0
3
[ "A000045", "A005181", "A019774" ]
[ "M0693" ]
N. J. A. Sloane, R. K. Guy
2025-02-16T08:32:28
oeisdata/seq/A005/A005181.seq
18544af2631803fd89dc55a99bf8e476
A005182
a(n) = floor(e^((n-1)/2)).
[ "0", "1", "1", "2", "4", "7", "12", "20", "33", "54", "90", "148", "244", "403", "665", "1096", "1808", "2980", "4914", "8103", "13359", "22026", "36315", "59874", "98715", "162754", "268337", "442413", "729416", "1202604", "1982759", "3269017", "5389698", "8886110", "14650719", "24154952", "39824784" ]
[ "nonn" ]
25
0
4
null
[ "M1057" ]
N. J. A. Sloane, R. K. Guy
2017-06-26T23:00:56
oeisdata/seq/A005/A005182.seq
d3473d8488922f74224cbb4a0897b049
A005183
a(n) = n*2^(n-1) + 1.
[ "1", "2", "5", "13", "33", "81", "193", "449", "1025", "2305", "5121", "11265", "24577", "53249", "114689", "245761", "524289", "1114113", "2359297", "4980737", "10485761", "22020097", "46137345", "96468993", "201326593", "419430401", "872415233", "1811939329", "3758096385", "7784628225", "16106127361", "33285996545" ]
[ "nonn", "easy" ]
110
0
2
[ "A000079", "A000120", "A000788", "A005183", "A028310", "A030190", "A030303", "A066099", "A134399" ]
[ "M1434" ]
N. J. A. Sloane, R. K. Guy
2024-05-15T10:39:33
oeisdata/seq/A005/A005183.seq
aff32e9c15a6626d96eb3311719eb6be
A005184
Self-contained numbers: odd numbers k whose Collatz sequence contains a higher multiple of k.
[ "31", "83", "293", "347", "671", "19151", "2025797" ]
[ "nonn", "more" ]
51
1
1
[ "A005184", "A059198" ]
[ "M5220" ]
N. J. A. Sloane
2021-11-24T03:04:11
oeisdata/seq/A005/A005184.seq
df9a26efd566139cd9506da1ac386007
A005185
Hofstadter Q-sequence: a(1) = a(2) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2.
[ "1", "1", "2", "3", "3", "4", "5", "5", "6", "6", "6", "8", "8", "8", "10", "9", "10", "11", "11", "12", "12", "12", "12", "16", "14", "14", "16", "16", "16", "16", "20", "17", "17", "20", "21", "19", "20", "22", "21", "22", "23", "23", "24", "24", "24", "24", "24", "32", "24", "25", "30", "28", "26", "30", "30", "28", "32", "30", "32", "32", "32", "32", "40", "33", "31", "38", "35", "33", "39", "40", "37", "38", "40", "39" ]
[ "nonn", "nice", "look" ]
256
1
3
[ "A004001", "A005185", "A005206", "A005374", "A005375", "A005378", "A005379", "A070867", "A081827", "A226222", "A226244", "A226245", "A239913", "A244477", "A284019" ]
[ "M0438" ]
Simon Plouffe and N. J. A. Sloane, May 20 1991
2025-02-16T08:32:28
oeisdata/seq/A005/A005185.seq
6883dd13840d89d7369ec27c59127fb6
A005186
a(n) is the number of integers m which take n steps to reach 1 in '3x+1' problem.
[ "1", "1", "1", "1", "1", "2", "2", "4", "4", "6", "6", "8", "10", "14", "18", "24", "29", "36", "44", "58", "72", "91", "113", "143", "179", "227", "287", "366", "460", "578", "732", "926", "1174", "1489", "1879", "2365", "2988", "3780", "4788", "6049", "7628", "9635", "12190", "15409", "19452", "24561", "31025", "39229", "49580", "62680", "79255", "100144" ]
[ "nonn", "easy", "nice" ]
144
0
6
[ "A005186", "A088975", "A176014", "A176866" ]
[ "M0305" ]
N. J. A. Sloane, R. K. Guy
2024-09-07T16:27:54
oeisdata/seq/A005/A005186.seq
ecf2098131dc66502934130f281a76ad
A005187
a(n) = a(floor(n/2)) + n; also denominators in expansion of 1/sqrt(1-x) are 2^a(n); also 2n - number of 1's in binary expansion of 2n.
[ "0", "1", "3", "4", "7", "8", "10", "11", "15", "16", "18", "19", "22", "23", "25", "26", "31", "32", "34", "35", "38", "39", "41", "42", "46", "47", "49", "50", "53", "54", "56", "57", "63", "64", "66", "67", "70", "71", "73", "74", "78", "79", "81", "82", "85", "86", "88", "89", "94", "95", "97", "98", "101", "102", "104", "105", "109", "110", "112", "113", "116", "117", "119", "120", "127", "128" ]
[ "nonn", "easy", "nice" ]
255
0
3
[ "A000120", "A000165", "A000225", "A001511", "A001790", "A004128", "A004134", "A005187", "A010050", "A011371", "A030308", "A046161", "A054899", "A055938", "A067080", "A079559", "A085354", "A098844", "A122247", "A132027" ]
[ "M2330" ]
N. J. A. Sloane, May 20 1991; Allan Wilks, Dec 11 1999
2025-03-01T12:11:38
oeisdata/seq/A005/A005187.seq
929a3182e6f3fd8c3b4afd25fe06920f
A005188
Armstrong (or pluperfect, or Plus Perfect, or narcissistic) numbers: m-digit positive numbers equal to sum of the m-th powers of their digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "153", "370", "371", "407", "1634", "8208", "9474", "54748", "92727", "93084", "548834", "1741725", "4210818", "9800817", "9926315", "24678050", "24678051", "88593477", "146511208", "472335975", "534494836", "912985153", "4679307774", "32164049650", "32164049651" ]
[ "nonn", "base", "fini", "full", "nice", "changed" ]
156
1
2
[ "A001694", "A003321", "A005188", "A005934", "A007532", "A010343", "A010354", "A014576", "A023052", "A046074", "A151543" ]
[ "M0488" ]
N. J. A. Sloane, Robert G. Wilson v
2025-04-20T20:13:06
oeisdata/seq/A005/A005188.seq
5d24617f79569835d5789f88e4312a0a
A005189
Number of n-term 2-sided generalized Fibonacci sequences.
[ "1", "1", "1", "3", "14", "85", "626", "5387", "52882", "582149", "7094234", "94730611", "1374650042", "21529197077", "361809517954", "6492232196699", "123852300381986", "2502521367966277", "53379537613065002", "1198434678728086019", "28245547605034208074", "697186985180529270101" ]
[ "nonn" ]
44
0
4
null
[ "M2976" ]
N. J. A. Sloane, Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005189.seq
e5624c88bbae41b971db285373764739
A005190
Central quadrinomial coefficients: largest coefficient of (1 + x + x^2 + x^3)^n.
[ "1", "1", "4", "12", "44", "155", "580", "2128", "8092", "30276", "116304", "440484", "1703636", "6506786", "25288120", "97181760", "379061020", "1463609356", "5724954544", "22187304112", "86981744944", "338118529539", "1327977811076", "5175023913008", "20356299454276" ]
[ "nonn", "easy" ]
64
0
3
[ "A005190", "A005721", "A005723", "A077042" ]
[ "M3456" ]
N. J. A. Sloane
2025-03-19T08:03:07
oeisdata/seq/A005/A005190.seq
e7ed3eeabff92847623c578b04b520fe
A005191
Central pentanomial coefficients: largest coefficient of (1 + x + ... + x^4)^n.
[ "1", "1", "5", "19", "85", "381", "1751", "8135", "38165", "180325", "856945", "4091495", "19611175", "94309099", "454805755", "2198649549", "10651488789", "51698642405", "251345549849", "1223798004815", "5966636799745", "29125608152345", "142330448514875", "696235630761115", "3408895901222375" ]
[ "nonn" ]
130
0
3
[ "A005191", "A035343", "A077042", "A201551", "A349936" ]
[ "M3891" ]
N. J. A. Sloane
2025-03-19T08:03:35
oeisdata/seq/A005/A005191.seq
199168474c39bd83de4dd837a82769bc
A005192
Finite difference measurements.
[ "1", "3", "18", "172", "2433" ]
[ "nonn", "more" ]
14
2
2
null
[ "M3051" ]
N. J. A. Sloane
2023-10-27T05:46:31
oeisdata/seq/A005/A005192.seq
b29c2bcf63885c8d4ca96ec5fcf85193
A005193
a(n) is the number of alpha-labelings of graphs with n edges.
[ "1", "2", "4", "10", "30", "106", "426", "1930", "9690", "53578", "322650", "2106250", "14790810", "111327178", "893091930", "7614236170", "68695024410", "654301474378", "6557096219610", "69005893630090", "760519875693210", "8763511069234378", "105343011537811290", "1319139904954848010" ]
[ "nonn" ]
57
1
2
[ "A005193", "A034384", "A342225" ]
[ "M1231" ]
N. J. A. Sloane
2023-10-28T15:28:42
oeisdata/seq/A005/A005193.seq
4fe5d0642f28527ab23a5018e6730919
A005194
Number of balanced symmetric graphs.
[ "1", "2", "4", "6", "10", "22", "38", "102", "182", "574", "1070", "3798", "7286", "28894", "57374", "248502", "506678", "2384254", "5007230", "25247958", "54311126", "292500574", "645652574", "3680048502", "8301671798", "49967727934", "115334270270", "728281984278", "1714641313046", "11341092707614" ]
[ "nonn" ]
21
1
2
null
[ "M1017" ]
N. J. A. Sloane
2023-10-28T09:33:16
oeisdata/seq/A005/A005194.seq
d56b6f88d7110d7f91fe87f232b71163
A005195
Number of forests with n unlabeled nodes.
[ "1", "1", "2", "3", "6", "10", "20", "37", "76", "153", "329", "710", "1601", "3658", "8599", "20514", "49905", "122963", "307199", "775529", "1977878", "5086638", "13184156", "34402932", "90328674", "238474986", "632775648", "1686705630", "4514955632", "12132227370", "32717113805", "88519867048", "240235675303" ]
[ "nonn", "easy", "nice" ]
67
0
3
[ "A000055", "A000088", "A000272", "A001858", "A002494", "A002807", "A005195", "A006125", "A006129", "A006785", "A054548", "A095133", "A105784", "A136605", "A137917", "A144215", "A144958", "A236570", "A367863", "A372169", "A372176", "A372191", "A372193", "A372195" ]
[ "M0776" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005195.seq
447062e00f704a61b30013f80f8b854e
A005196
a(n) = Sum_t t*F(n,t), where F(n,t) (see A095133) is the number of forests with n (unlabeled) nodes and exactly t trees.
[ "1", "3", "6", "13", "24", "49", "93", "190", "381", "803", "1703", "3755", "8401", "19338", "45275", "108229", "262604", "647083", "1613941", "4072198", "10374138", "26663390", "69056163", "180098668", "472604314", "1247159936", "3307845730", "8814122981", "23585720703", "63359160443", "170815541708", "462049250165" ]
[ "nonn", "nice" ]
45
1
2
[ "A000055", "A005195", "A005196", "A095133" ]
[ "M2567" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005196.seq
b4b533af73df31b9915dd7cfa2f6dc4f
A005197
a(n) = Sum_t t*F(n,t), where F(n,t) (see A033185) is the number of rooted forests with n (unlabeled) nodes and exactly t rooted trees.
[ "1", "3", "7", "17", "39", "96", "232", "583", "1474", "3797", "9864", "25947", "68738", "183612", "493471", "1334143", "3624800", "9893860", "27113492", "74577187", "205806860", "569678759", "1581243203", "4400193551", "12273287277", "34307646762", "96093291818", "269654004899", "758014312091", "2134300171031" ]
[ "nonn" ]
32
1
2
[ "A000081", "A005196", "A005197", "A033185" ]
[ "M2663" ]
N. J. A. Sloane. Definition clarified by N. J. A. Sloane, May 29 2012
2017-08-25T16:39:28
oeisdata/seq/A005/A005197.seq
c3a2ed4a9a2f934007ece7bc60b1125e
A005198
a(n) is the number of forests with n (unlabeled) nodes in which each component tree is planted, that is, is a rooted tree in which the root has degree 1.
[ "0", "1", "1", "3", "5", "13", "27", "68", "160", "404", "1010", "2604", "6726", "17661", "46628", "124287", "333162", "898921", "2437254", "6640537", "18166568", "49890419", "137478389", "380031868", "1053517588", "2928246650", "8158727139", "22782938271", "63752461474", "178740014515", "502026565792", "1412409894224" ]
[ "nonn" ]
35
1
4
[ "A000081", "A005198" ]
[ "M2491" ]
N. J. A. Sloane
2023-10-27T05:53:22
oeisdata/seq/A005/A005198.seq
a4868e88e7fd926a85198f6f4237a9b0
A005199
a(n) = Sum_t t*F(n,t), where F(n,t) is the number of forests with n (unlabeled) nodes and exactly t trees, all of which are planted (that is, rooted trees in which the root has degree 1).
[ "0", "1", "1", "4", "6", "18", "35", "93", "214", "549", "1362", "3534", "9102", "23951", "63192", "168561", "451764", "1219290", "3305783", "9008027", "24643538", "67681372", "186504925", "515566016", "1429246490", "3972598378", "11068477743", "30908170493", "86488245455", "242481159915", "681048784377", "1916051725977", "5399062619966" ]
[ "nonn" ]
23
1
4
[ "A000081", "A005199", "A336087" ]
[ "M3285" ]
N. J. A. Sloane
2020-08-02T21:20:41
oeisdata/seq/A005/A005199.seq
ded212e388cb9df993f678c5e6c43b29
A005200
Total number of fixed points in rooted trees with n nodes.
[ "1", "2", "4", "11", "28", "78", "213", "598", "1670", "4723", "13356", "37986", "108193", "309169", "884923", "2538369", "7292170", "20982220", "60451567", "174385063", "503600439", "1455827279", "4212464112", "12199373350", "35357580112", "102552754000", "297651592188", "864460682777", "2512115979800", "7304240074858" ]
[ "nonn", "easy", "nice" ]
43
1
2
[ "A000055", "A000081", "A005200", "A005201" ]
[ "M1247" ]
N. J. A. Sloane
2023-10-27T19:39:46
oeisdata/seq/A005/A005200.seq
6c0f798b7bc8d6037fb9f24c18337566