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score
int64
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2.35k
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int64
-14,827
666,262,453B
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int64
0
635M
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A363601
Number of partitions of n where there are k^2 - 1 kinds of parts k.
[ "1", "0", "3", "8", "21", "48", "126", "288", "693", "1568", "3570", "7896", "17417", "37632", "80823", "171192", "359733", "747936", "1543192", "3155760", "6407037", "12909024", "25835649", "51359136", "101470854", "199264128", "389096028", "755591256", "1459643343", "2805471984", "5366161740", "10216161336", "19362398580" ]
[ "nonn", "easy" ]
27
0
3
[ "A005380", "A023871", "A052847", "A092348", "A120844", "A217093", "A253289", "A255271", "A255802", "A255803", "A255835", "A255836", "A363601", "A363602" ]
null
Seiichi Manyama, Jun 10 2023
2025-01-16T11:29:56
oeisdata/seq/A363/A363601.seq
9078a21477f31485e797d8837b6e33c5
A363602
Number of partitions of n where there are k^2+1 kinds of parts k.
[ "1", "2", "8", "24", "72", "196", "532", "1368", "3467", "8520", "20580", "48664", "113330", "259588", "586692", "1308304", "2883427", "6283192", "13551344", "28940688", "61246052", "128492516", "267388008", "552126648", "1131750735", "2303690862", "4658080756", "9358912416", "18689701580", "37106245300", "73259451208" ]
[ "nonn", "easy" ]
18
0
2
[ "A023871", "A092345", "A363601", "A363602" ]
null
Seiichi Manyama, Jun 10 2023
2023-06-11T11:15:07
oeisdata/seq/A363/A363602.seq
f4cc5097df05228e0e85f659a146aaac
A363603
Expansion of e.g.f. (1/4)*(exp(x)-x-1)*(exp(x)-1)^2.
[ "3", "20", "90", "343", "1197", "3966", "12720", "39941", "123651", "379132", "1154790", "3501219", "10581465", "31908218", "96068700", "288926977", "868288239", "2608010424", "7830584850", "23505386015", "70544469573", "211692128950", "635198021640", "1905845723133", "5718057263067" ]
[ "nonn", "easy" ]
33
4
1
[ "A000225", "A001117", "A052749", "A363591", "A363603" ]
null
Enrique Navarrete, Jun 11 2023
2023-11-18T18:08:57
oeisdata/seq/A363/A363603.seq
ca61f0dc4a351ac6bee37a20c6d6292c
A363604
Expansion of Sum_{k>0} x^(2*k)/(1-x^k)^4.
[ "0", "1", "4", "11", "20", "40", "56", "95", "124", "186", "220", "336", "364", "512", "584", "775", "816", "1129", "1140", "1526", "1600", "1992", "2024", "2720", "2620", "3290", "3400", "4176", "4060", "5280", "4960", "6231", "6208", "7362", "7216", "9195", "8436", "10280", "10248", "12270", "11480", "14432", "13244", "16192", "15884", "18240" ]
[ "nonn", "easy" ]
31
1
3
[ "A000203", "A000292", "A001158", "A013662", "A032741", "A059358", "A065608", "A069153", "A092348", "A363604", "A363605", "A363606", "A363607", "A363611" ]
null
Seiichi Manyama, Jun 11 2023
2024-12-30T02:16:14
oeisdata/seq/A363/A363604.seq
af3b81dfc0cc848258b0ac37951f8171
A363605
Expansion of Sum_{k>0} x^(2*k)/(1-x^k)^5.
[ "0", "1", "5", "16", "35", "76", "126", "226", "335", "531", "715", "1092", "1365", "1947", "2420", "3286", "3876", "5251", "5985", "7861", "8986", "11342", "12650", "16252", "17585", "21841", "24086", "29367", "31465", "38946", "40920", "49662", "53080", "62782", "66206", "80082", "82251", "97376", "102640", "120001", "123410", "146628" ]
[ "nonn", "easy" ]
19
1
3
[ "A000203", "A001157", "A001158", "A001159", "A013663", "A032741", "A065608", "A069153", "A363604", "A363605", "A363606" ]
null
Seiichi Manyama, Jun 11 2023
2024-12-30T02:16:22
oeisdata/seq/A363/A363605.seq
cfaccb5359db9549fb5bb2457272f68e
A363606
Expansion of Sum_{k>0} x^(2*k)/(1-x^k)^6.
[ "0", "1", "6", "22", "56", "133", "252", "484", "798", "1344", "2002", "3157", "4368", "6441", "8630", "12112", "15504", "21274", "26334", "35014", "42762", "55133", "65780", "84349", "98336", "123124", "143304", "176373", "201376", "247380", "278256", "336744", "379000", "451402", "502250", "600055", "658008", "775733", "855042" ]
[ "nonn", "easy" ]
22
1
3
[ "A000203", "A001157", "A001158", "A001159", "A001160", "A013664", "A032741", "A065608", "A069153", "A363604", "A363605", "A363606" ]
null
Seiichi Manyama, Jun 11 2023
2024-12-30T02:16:29
oeisdata/seq/A363/A363606.seq
68f0503218c11c414ea3c9c1bbf359ed
A363607
Expansion of Sum_{k>0} x^(3*k)/(1-x^k)^4.
[ "0", "0", "1", "4", "10", "21", "35", "60", "85", "130", "165", "245", "286", "399", "466", "620", "680", "921", "969", "1274", "1366", "1705", "1771", "2325", "2310", "2886", "3010", "3679", "3654", "4666", "4495", "5580", "5622", "6664", "6590", "8285", "7770", "9405", "9426", "11210", "10660", "13230", "12341", "14953", "14740", "16951", "16215", "20181" ]
[ "nonn", "easy" ]
25
1
4
[ "A000203", "A001157", "A001158", "A013662", "A059358", "A069153", "A363604", "A363607", "A363608", "A363611" ]
null
Seiichi Manyama, Jun 11 2023
2024-12-30T02:16:36
oeisdata/seq/A363/A363607.seq
943de3bf8c89211e495c6ed75d9bc865
A363608
Expansion of Sum_{k>0} x^(4*k)/(1-x^k)^5.
[ "0", "0", "0", "1", "5", "15", "35", "71", "126", "215", "330", "511", "715", "1036", "1370", "1891", "2380", "3201", "3876", "5061", "6020", "7645", "8855", "11207", "12655", "15665", "17676", "21512", "23751", "29000", "31465", "37851", "41250", "48756", "52400", "62602", "66045", "77691", "82966", "96521", "101270", "118966", "123410", "143397" ]
[ "nonn", "easy" ]
22
1
5
[ "A000203", "A001157", "A001158", "A001159", "A013663", "A069153", "A363607", "A363608" ]
null
Seiichi Manyama, Jun 11 2023
2024-12-30T02:16:45
oeisdata/seq/A363/A363608.seq
6035130ebe5d97d36e92b82a20c69399
A363609
Minimum sum of the visible pips on a polycube made from n dice.
[ "21", "30", "40", "40", "51", "52", "54", "48", "60", "62", "65", "60", "72", "74", "77", "72", "78", "74", "86", "84", "91", "88", "92", "88", "95", "93", "90", "102", "105", "102", "106", "104", "107", "110", "109", "106", "118", "120", "121", "120", "125", "123", "126", "125", "122", "128", "127", "124", "136", "138", "139", "140", "141", "138", "145", "144", "143" ]
[ "nonn" ]
45
1
1
[ "A193416", "A363609" ]
null
Matt Donahoe, Jun 11 2023
2023-09-03T10:23:35
oeisdata/seq/A363/A363609.seq
9d6b2f9c32207c992e9f289ce214142c
A363610
Expansion of Sum_{k>0} x^(3*k)/(1-x^k)^3.
[ "0", "0", "1", "3", "6", "11", "15", "24", "29", "42", "45", "69", "66", "93", "98", "129", "120", "175", "153", "216", "206", "255", "231", "343", "282", "366", "354", "447", "378", "550", "435", "594", "542", "648", "582", "828", "630", "819", "770", "978", "780", "1114", "861", "1161", "1072", "1221", "1035", "1529", "1143", "1494", "1346", "1644", "1326", "1878", "1482", "1953" ]
[ "nonn", "easy" ]
24
1
4
[ "A000005", "A000203", "A001157", "A002117", "A007437", "A065608", "A069153", "A363610", "A363611" ]
null
Seiichi Manyama, Jun 11 2023
2025-01-02T09:35:48
oeisdata/seq/A363/A363610.seq
e2e1b3b83fadc2746e3c04dcaa806eae
A363611
Expansion of Sum_{k>0} x^(4*k)/(1-x^k)^4.
[ "0", "0", "0", "1", "4", "10", "20", "36", "56", "88", "120", "176", "220", "306", "368", "491", "560", "746", "816", "1058", "1160", "1450", "1540", "1982", "2028", "2520", "2656", "3232", "3276", "4116", "4060", "4986", "5080", "6016", "6008", "7457", "7140", "8586", "8656", "10232", "9880", "12116", "11480", "13792", "13668", "15730", "15180", "18652", "17316", "20536" ]
[ "nonn", "easy" ]
33
1
5
[ "A000005", "A000203", "A001157", "A001158", "A013662", "A059358", "A065608", "A363604", "A363607", "A363610", "A363611" ]
null
Seiichi Manyama, Jun 11 2023
2025-01-02T09:35:59
oeisdata/seq/A363/A363611.seq
67fe890559ce8ad9401ac78a28fcc9e3
A363612
Number of iterations of phi(x) at n needed to reach a square.
[ "0", "1", "2", "0", "1", "2", "3", "1", "0", "1", "2", "1", "2", "3", "2", "0", "1", "3", "4", "2", "2", "2", "3", "2", "0", "2", "4", "2", "3", "2", "3", "1", "3", "1", "3", "0", "1", "4", "3", "1", "2", "2", "3", "3", "3", "3", "4", "1", "0", "3", "2", "3", "4", "4", "2", "3", "1", "3", "4", "1", "2", "3", "1", "0", "2", "3", "4", "2", "4", "3", "4", "3", "4", "1", "2", "1", "2", "3", "4", "2", "0", "2", "3", "3", "1", "3", "4" ]
[ "nonn" ]
21
1
3
[ "A000010", "A003434", "A363612" ]
null
Darío Clavijo, Jun 11 2023
2023-06-15T10:49:36
oeisdata/seq/A363/A363612.seq
032ae8618d907da494e539f52ea31a7d
A363613
Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^5.
[ "0", "1", "-5", "16", "-35", "66", "-126", "226", "-335", "461", "-715", "1082", "-1365", "1695", "-2420", "3286", "-3876", "4581", "-5985", "7791", "-8986", "9912", "-12650", "16242", "-17585", "19111", "-24086", "29115", "-31465", "34106", "-40920", "49662", "-53080", "55030", "-66206", "79412", "-82251", "85406", "-102640", "119931" ]
[ "sign" ]
18
1
3
[ "A325940", "A363022", "A363598", "A363605", "A363613", "A363614" ]
null
Seiichi Manyama, Jun 11 2023
2023-07-25T17:17:19
oeisdata/seq/A363/A363613.seq
26fbd5d54a60d88eaf243638b609d80a
A363614
Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^6.
[ "0", "1", "-6", "22", "-56", "121", "-252", "484", "-798", "1232", "-2002", "3145", "-4368", "5937", "-8630", "12112", "-15504", "19678", "-26334", "34902", "-42762", "51129", "-65780", "84337", "-98336", "114388", "-143304", "175869", "-201376", "230120", "-278256", "336744", "-379000", "420394", "-502250", "598459", "-658008", "723065", "-855042", "997962", "-1086008" ]
[ "sign" ]
19
1
3
[ "A325940", "A363022", "A363598", "A363606", "A363613", "A363614" ]
null
Seiichi Manyama, Jun 11 2023
2023-07-19T02:19:46
oeisdata/seq/A363/A363614.seq
d3d7cfb8ffaecdc6bd9675b6eca44ca6
A363615
Expansion of Sum_{k>0} x^(3*k)/(1+x^k)^3.
[ "0", "0", "1", "-3", "6", "-9", "15", "-24", "29", "-30", "45", "-67", "66", "-63", "98", "-129", "120", "-117", "153", "-204", "206", "-165", "231", "-341", "282", "-234", "354", "-417", "378", "-354", "435", "-594", "542", "-408", "582", "-770", "630", "-513", "770", "-966", "780", "-702", "861", "-1071", "1072", "-759", "1035", "-1527", "1143", "-930", "1346" ]
[ "sign" ]
31
1
4
[ "A002129", "A048272", "A128315", "A321543", "A325940", "A363610", "A363615", "A363616" ]
null
Seiichi Manyama, Jun 11 2023
2025-01-04T05:37:50
oeisdata/seq/A363/A363615.seq
6cae8ba92429bad4475a569b34d64c20
A363616
Expansion of Sum_{k>0} x^(4*k)/(1+x^k)^4.
[ "0", "0", "0", "1", "-4", "10", "-20", "36", "-56", "80", "-120", "176", "-220", "266", "-368", "491", "-560", "634", "-816", "1050", "-1160", "1210", "-1540", "1982", "-2028", "2080", "-2656", "3192", "-3276", "3380", "-4060", "4986", "-5080", "4896", "-6008", "7345", "-7140", "6954", "-8656", "10224", "-9880", "9796", "-11480", "13552", "-13668", "12650" ]
[ "sign" ]
30
1
5
[ "A002129", "A128315", "A138503", "A321543", "A325940", "A363611", "A363615", "A363616" ]
null
Seiichi Manyama, Jun 11 2023
2025-01-04T05:46:27
oeisdata/seq/A363/A363616.seq
ede443db47cce5382337947b9828aeaa
A363617
Expansion of Sum_{k>0} x^(3*k)/(1+x^k)^4.
[ "0", "0", "1", "-4", "10", "-19", "35", "-60", "85", "-110", "165", "-243", "286", "-329", "466", "-620", "680", "-751", "969", "-1254", "1366", "-1375", "1771", "-2323", "2310", "-2314", "3010", "-3609", "3654", "-3734", "4495", "-5580", "5622", "-5304", "6590", "-8115", "7770", "-7467", "9426", "-11190", "10660", "-10498", "12341", "-14623", "14740", "-13409", "16215", "-20179", "18459", "-17410", "21506" ]
[ "sign" ]
18
1
4
[ "A363022", "A363607", "A363617", "A363618" ]
null
Seiichi Manyama, Jun 11 2023
2023-07-19T02:19:53
oeisdata/seq/A363/A363617.seq
48f4dba62fe355852e7b2caafce51bda
A363618
Expansion of Sum_{k>0} x^(4*k)/(1+x^k)^5.
[ "0", "0", "0", "1", "-5", "15", "-35", "71", "-126", "205", "-330", "511", "-715", "966", "-1370", "1891", "-2380", "2949", "-3876", "5051", "-6020", "6985", "-8855", "11207", "-12655", "14235", "-17676", "21442", "-23751", "26260", "-31465", "37851", "-41250", "43996", "-52400", "62350", "-66045", "69939", "-82966", "96511", "-101270" ]
[ "sign" ]
17
1
5
[ "A363022", "A363608", "A363617", "A363618" ]
null
Seiichi Manyama, Jun 11 2023
2023-07-25T16:37:51
oeisdata/seq/A363/A363618.seq
498d27972a6fdce4fee02173e21af366
A363619
Weighted alternating sum of the multiset of prime indices of n.
[ "0", "1", "2", "-1", "3", "-3", "4", "2", "-2", "-5", "5", "5", "6", "-7", "-4", "-2", "7", "3", "8", "8", "-6", "-9", "9", "-6", "-3", "-11", "4", "11", "10", "6", "11", "3", "-8", "-13", "-5", "-3", "12", "-15", "-10", "-10", "13", "9", "14", "14", "7", "-17", "15", "8", "-4", "4", "-12", "17", "16", "-5", "-7", "-14", "-14", "-19", "17", "-7", "18", "-21", "10", "-3", "-9", "12", "19", "20" ]
[ "sign" ]
14
1
3
[ "A000009", "A000720", "A001221", "A001222", "A046660", "A053632", "A055396", "A056239", "A061395", "A106529", "A112798", "A124010", "A181819", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A358194", "A359674", "A359677", "A359678", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 12 2023
2023-08-16T10:59:06
oeisdata/seq/A363/A363619.seq
aba147d70be6ff34983e1cd2d3280814
A363620
Reverse-weighted alternating sum of the multiset of prime indices of n.
[ "0", "1", "2", "1", "3", "0", "4", "2", "2", "-1", "5", "3", "6", "-2", "1", "2", "7", "1", "8", "4", "0", "-3", "9", "1", "3", "-4", "4", "5", "10", "2", "11", "3", "-1", "-5", "2", "3", "12", "-6", "-2", "0", "13", "3", "14", "6", "5", "-7", "15", "4", "4", "0", "-3", "7", "16", "0", "1", "-1", "-4", "-8", "17", "2", "18", "-9", "6", "3", "0", "4", "19", "8", "-5", "1", "20", "2", "21", "-10", "3", "9", "3" ]
[ "sign" ]
13
1
3
[ "A001221", "A001222", "A046660", "A053632", "A055396", "A056239", "A061395", "A106529", "A112798", "A124010", "A222855", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A358136", "A358137", "A358194", "A359361", "A359674", "A359678", "A359755", "A363531", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625" ]
null
Gus Wiseman, Jun 13 2023
2023-08-16T10:59:23
oeisdata/seq/A363/A363620.seq
c7534f337fc540b206fc9870fe891351
A363621
Positive integers whose prime indices have reverse-weighted alternating sum 0.
[ "1", "6", "21", "40", "50", "54", "65", "132", "133", "154", "210", "224", "319", "340", "351", "360", "374", "392", "450", "481", "486", "507", "546", "598", "624", "644", "731", "825", "855", "969", "1007", "1029", "1054", "1144", "1210", "1254", "1320", "1364", "1386", "1403", "1408", "1520", "1558", "1653", "1750", "1785", "1827", "1836", "1890", "1960" ]
[ "nonn" ]
10
1
2
[ "A000290", "A001222", "A046660", "A053632", "A055396", "A056239", "A061395", "A106529", "A112798", "A124010", "A181819", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A358194", "A359674", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 13 2023
2023-06-15T07:32:55
oeisdata/seq/A363/A363621.seq
962cb26402929d9776bf29309dd22113
A363622
Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with weighted alternating sum k (leading and trailing 0's omitted).
[ "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "2", "0", "0", "1", "0", "1", "1", "2", "0", "1", "1", "1", "1", "1", "3", "0", "0", "2", "0", "1", "1", "2", "1", "1", "3", "0", "2", "2", "1", "1", "2", "2", "1", "1", "5", "0", "0", "3", "0", "2", "2", "2", "1", "3", "2", "1", "1", "5", "0", "3", "3", "2", "2", "3", "2", "2", "4", "2", "1", "1", "7", "0", "0", "5", "0", "3", "3", "4", "2", "4", "2", "4", "4", "2", "1", "1" ]
[ "nonn", "tabf" ]
7
0
11
[ "A000041", "A008284", "A053632", "A067538", "A103919", "A168233", "A222855", "A222970", "A264034", "A316524", "A318283", "A320387", "A344616", "A358194", "A360672", "A360675", "A362559", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 15 2023
2023-06-15T20:06:52
oeisdata/seq/A363/A363622.seq
7c209203378ebe27bf4de9a618900b7d
A363623
Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with reverse-weighted alternating sum k (leading and trailing 0's omitted).
[ "1", "1", "1", "1", "1", "2", "2", "0", "1", "2", "2", "1", "1", "1", "1", "1", "3", "1", "0", "3", "0", "1", "1", "1", "1", "3", "2", "0", "3", "1", "2", "0", "1", "0", "1", "2", "5", "1", "0", "3", "1", "2", "2", "2", "1", "1", "0", "1", "0", "1", "2", "5", "3", "0", "4", "2", "2", "0", "3", "2", "1", "3", "0", "0", "1", "0", "1", "1", "1", "1", "7", "2", "0", "4", "1", "5", "2", "3", "1", "3", "0", "2", "3", "1", "2", "1", "0", "0", "1", "0", "1", "1", "1", "1" ]
[ "nonn", "tabf" ]
4
0
6
[ "A000041", "A008284", "A053632", "A067538", "A103919", "A119620", "A222855", "A222970", "A264034", "A316524", "A318283", "A320387", "A344612", "A344616", "A358194", "A360672", "A360675", "A362559", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 15 2023
2023-06-15T20:06:48
oeisdata/seq/A363/A363623.seq
4349241803fb7f748e709734def50745
A363624
Weighted alternating sum of the integer partition with Heinz number n.
[ "0", "1", "2", "-1", "3", "0", "4", "2", "-2", "1", "5", "3", "6", "2", "-1", "-2", "7", "1", "8", "4", "0", "3", "9", "-1", "-3", "4", "4", "5", "10", "2", "11", "3", "1", "5", "-2", "-3", "12", "6", "2", "0", "13", "3", "14", "6", "5", "7", "15", "4", "-4", "0", "3", "7", "16", "0", "-1", "1", "4", "8", "17", "-2", "18", "9", "6", "-3", "0", "4", "19", "8", "5", "1", "20", "2", "21", "10", "3", "9", "-3", "5" ]
[ "sign" ]
11
1
3
[ "A001222", "A007294", "A046660", "A053632", "A055396", "A056239", "A061395", "A106529", "A112798", "A124010", "A215366", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A358136", "A358194", "A359361", "A359674", "A359677", "A359755", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 13 2023
2023-08-16T10:59:42
oeisdata/seq/A363/A363624.seq
4a4b9bb70d689fc5981ae252015ffab8
A363625
Reverse-weighted alternating sum of the integer partition with Heinz number n.
[ "0", "1", "2", "1", "3", "3", "4", "2", "2", "5", "5", "5", "6", "7", "4", "2", "7", "3", "8", "8", "6", "9", "9", "6", "3", "11", "4", "11", "10", "6", "11", "3", "8", "13", "5", "3", "12", "15", "10", "10", "13", "9", "14", "14", "7", "17", "15", "8", "4", "4", "12", "17", "16", "5", "7", "14", "14", "19", "17", "7", "18", "21", "10", "3", "9", "12", "19", "20", "16", "7", "20", "4", "21", "23", "5", "23" ]
[ "nonn" ]
8
1
3
[ "A001222", "A007294", "A046660", "A053632", "A055396", "A056239", "A061395", "A106529", "A112798", "A124010", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A358194", "A359361", "A359755", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 15 2023
2023-08-16T11:00:07
oeisdata/seq/A363/A363625.seq
7e16abff326f8c05ea1e5b1608b0cee3
A363626
Number of integer compositions of n with weighted alternating sum 0.
[ "1", "0", "0", "1", "1", "0", "2", "5", "7", "8", "14", "38", "64", "87", "174", "373", "649", "1069", "2051", "4091", "7453", "13276", "25260", "48990", "91378", "168890", "321661", "618323", "1169126", "2203649", "4211163", "8085240", "15421171", "29390131", "56382040", "108443047", "208077560", "399310778" ]
[ "nonn" ]
16
0
7
[ "A000041", "A008284", "A053632", "A106529", "A138364", "A261079", "A264034", "A304818", "A316524", "A318283", "A320387", "A344616", "A344619", "A358194", "A360672", "A360675", "A362559", "A363532", "A363619", "A363620", "A363621", "A363622", "A363623", "A363624", "A363625", "A363626" ]
null
Gus Wiseman, Jun 16 2023
2023-09-05T15:21:20
oeisdata/seq/A363/A363626.seq
32b42dcf1f4d4eb9e01b459266e407e6
A363627
a(n) = greatest product < n of some subset of the divisors of n, or if n is in A008578 then a(n) = n.
[ "1", "2", "3", "2", "5", "3", "7", "4", "3", "5", "11", "8", "13", "7", "5", "8", "17", "12", "19", "10", "7", "11", "23", "18", "5", "13", "9", "14", "29", "20", "31", "16", "11", "17", "7", "27", "37", "19", "13", "32", "41", "36", "43", "22", "27", "23", "47", "36", "7", "25", "17", "26", "53", "36", "11", "32" ]
[ "nonn" ]
18
1
2
[ "A008578", "A363501", "A363627" ]
null
Denis Ivanov, Jun 12 2023
2023-06-17T14:22:48
oeisdata/seq/A363/A363627.seq
6546fa7dfda50045ab717646ac2c038e
A363628
Expansion of Sum_{k>0} (1/(1-x^k)^3 - 1).
[ "3", "9", "13", "24", "24", "47", "39", "69", "68", "96", "81", "153", "108", "165", "170", "222", "174", "292", "213", "342", "302", "363", "303", "523", "375", "492", "474", "615", "468", "766", "531", "783", "686", "810", "726", "1101", "744", "999", "938", "1248", "906", "1402", "993", "1413", "1306", "1437", "1179", "1901", "1314", "1773", "1562", "1938", "1488", "2238", "1698" ]
[ "nonn", "easy" ]
13
1
1
[ "A007437", "A007503", "A069153", "A116963", "A363610", "A363628" ]
null
Seiichi Manyama, Jun 12 2023
2023-07-05T01:45:22
oeisdata/seq/A363/A363628.seq
f6ed2a73850a69d1c932b104f5aa296e
A363629
Expansion of Sum_{k>0} (1/(1+x^k)^2 - 1).
[ "-2", "1", "-6", "6", "-8", "4", "-10", "15", "-16", "6", "-14", "22", "-16", "8", "-28", "32", "-20", "13", "-22", "32", "-36", "12", "-26", "56", "-34", "14", "-44", "42", "-32", "24", "-34", "65", "-52", "18", "-52", "68", "-40", "20", "-60", "82", "-44", "32", "-46", "62", "-84", "24", "-50", "122", "-60", "31", "-76", "72", "-56", "40", "-76", "108", "-84", "30", "-62", "124", "-64", "32", "-110", "130", "-88", "48", "-70", "92" ]
[ "sign", "easy" ]
25
1
1
[ "A002129", "A048272", "A325940", "A363629", "A363630", "A363631" ]
null
Seiichi Manyama, Jun 12 2023
2023-07-19T02:19:56
oeisdata/seq/A363/A363629.seq
24b41cead9a4bc1f5559f2b470f14496
A363630
Expansion of Sum_{k>0} (1/(1+x^k)^3 - 1).
[ "-3", "3", "-13", "18", "-24", "21", "-39", "63", "-68", "48", "-81", "127", "-108", "87", "-170", "216", "-174", "156", "-213", "294", "-302", "201", "-303", "497", "-375", "276", "-474", "537", "-468", "426", "-531", "777", "-686", "462", "-726", "965", "-744", "573", "-938", "1200", "-906", "798", "-993", "1251", "-1306", "831", "-1179", "1875", "-1314", "1023", "-1562", "1722", "-1488", "1290", "-1698" ]
[ "sign", "easy" ]
21
1
1
[ "A002129", "A048272", "A320900", "A321543", "A363022", "A363615", "A363629", "A363630", "A363631" ]
null
Seiichi Manyama, Jun 12 2023
2025-01-04T06:15:11
oeisdata/seq/A363/A363630.seq
d7efd626d215f68b0a061d12eb2c1024
A363631
Expansion of Sum_{k>0} (1/(1+x^k)^4 - 1).
[ "-4", "6", "-24", "41", "-60", "70", "-124", "206", "-244", "236", "-368", "560", "-564", "566", "-896", "1175", "-1144", "1180", "-1544", "2042", "-2168", "1942", "-2604", "3650", "-3336", "3100", "-4304", "5096", "-4964", "4940", "-5988", "7720", "-7528", "6636", "-8616", "10809", "-9884", "9126", "-12064", "14548", "-13248", "12796", "-15184", "18192", "-18412", "15830" ]
[ "sign", "easy" ]
17
1
1
[ "A320901", "A363598", "A363616", "A363617", "A363629", "A363630", "A363631" ]
null
Seiichi Manyama, Jun 12 2023
2023-07-19T02:20:02
oeisdata/seq/A363/A363631.seq
369d19d0efee589d49cceed95b858919
A363632
Decimal expansion of Sum_{k>=2} 1/(k* log(k)^(3/2)).
[ "2", "9", "3", "7", "6", "6", "3", "6", "3", "7", "9", "0", "1", "2", "3", "1", "7", "7" ]
[ "cons", "nonn" ]
5
1
1
[ "A115563", "A145419", "A145420", "A363632", "A363633" ]
null
R. J. Mathar, Jun 12 2023
2023-06-12T07:37:18
oeisdata/seq/A363/A363632.seq
64f4c19f5921c5821349d868437ca22a
A363633
Decimal expansion of Sum_{k>=2} 1/(k* log(k)^(5/2)).
[ "1", "9", "8", "3", "4", "6", "3", "5", "4", "7", "1", "5", "6", "2", "3", "9", "3", "9", "1", "1", "8" ]
[ "cons", "nonn" ]
4
1
2
[ "A115563", "A145419", "A145420", "A363632", "A363633" ]
null
R. J. Mathar, Jun 12 2023
2023-06-12T07:38:31
oeisdata/seq/A363/A363633.seq
13886e00d3276694eff33ddda89d39b1
A363634
Lucky numbers that are products of smaller lucky numbers.
[ "1", "9", "21", "49", "63", "75", "93", "99", "105", "111", "129", "135", "169", "189", "195", "201", "219", "231", "237", "259", "261", "273", "297", "357", "399", "429", "477", "483", "489", "495", "511", "553", "559", "579", "615", "621", "645", "651", "693", "723", "729", "735", "777", "801", "805", "819", "855", "867", "897", "903", "925", "931", "957", "961" ]
[ "nonn" ]
8
1
2
[ "A000959", "A363634", "A363635", "A363636" ]
null
Pontus von Brömssen, Jun 19 2023
2023-07-15T06:36:02
oeisdata/seq/A363/A363634.seq
c29b012171d2ace161e5d49b26b277a8
A363635
Ludic numbers that are products of smaller ludic numbers.
[ "1", "25", "77", "91", "115", "119", "121", "143", "161", "175", "221", "235", "265", "287", "301", "329", "377", "407", "415", "445", "481", "493", "497", "517", "535", "581", "595", "625", "667", "697", "749", "805", "841", "851", "865", "913", "943", "1015", "1043", "1045", "1105", "1177", "1207", "1225", "1247", "1351", "1363", "1375", "1391", "1403" ]
[ "nonn" ]
5
1
2
[ "A003309", "A363634", "A363635", "A363636" ]
null
Pontus von Brömssen, Jun 19 2023
2023-07-15T06:36:10
oeisdata/seq/A363/A363635.seq
7ffe29947db68b5aa839b63f45abe739
A363636
Indices of numbers of the form k^2+1, k >= 0, that can be written as a product of smaller numbers of that same form.
[ "0", "3", "7", "13", "17", "18", "21", "31", "38", "43", "47", "57", "68", "73", "91", "99", "111", "117", "123", "132", "133", "157", "183", "211", "241", "242", "253", "255", "268", "273", "293", "302", "307", "313", "322", "327", "343", "381", "413", "421", "438", "443", "463", "487", "507", "515", "553", "557", "577", "593", "601", "651", "693", "697", "703", "707" ]
[ "nonn" ]
35
1
2
[ "A000027", "A000041", "A000142", "A000217", "A000292", "A000326", "A000330", "A000384", "A000959", "A002378", "A002411", "A002412", "A002522", "A003309", "A005563", "A006093", "A007531", "A008864", "A018252", "A034878", "A068143", "A363492", "A363634", "A363635", "A363636", "A363637", "A363638", "A363750", "A364151", "A374372", "A374373", "A374374", "A374375", "A374500", "A374501", "A374502" ]
null
Pontus von Brömssen, Jun 19 2023
2024-07-11T10:47:07
oeisdata/seq/A363/A363636.seq
af2b5a7ba1cf55cd021f513a6d6a8dba
A363637
Indices of numbers of the form k^2-1, k >= 2, that can be written as a product of smaller numbers of that same form.
[ "5", "11", "19", "26", "29", "31", "41", "55", "65", "71", "89", "99", "109", "127", "131", "134", "151", "155", "161", "181", "191", "209", "239", "244", "251", "265", "271", "274", "287", "289", "305", "323", "341", "349", "351", "379", "419", "449", "461", "485", "491", "505", "511", "551", "575", "599", "647", "649", "701", "703", "755", "769", "811", "846", "869" ]
[ "nonn" ]
4
1
1
[ "A005563", "A363636", "A363637" ]
null
Pontus von Brömssen, Jun 19 2023
2023-07-15T06:36:29
oeisdata/seq/A363/A363637.seq
14a5e029b99edb63410351d7807b79c6
A363638
Primes p such that p+1 can be written as a product of smaller numbers that are also of the form prime+1.
[ "11", "17", "23", "31", "41", "47", "53", "59", "71", "79", "83", "89", "107", "113", "127", "131", "151", "167", "179", "191", "223", "227", "239", "251", "263", "269", "271", "293", "311", "359", "383", "419", "431", "439", "443", "449", "479", "491", "503", "521", "557", "587", "593", "599", "607", "631", "647", "659", "683", "701", "719", "727", "743", "773" ]
[ "nonn" ]
6
1
1
[ "A008864", "A066938", "A363636", "A363638", "A363750" ]
null
Pontus von Brömssen, Jun 19 2023
2023-07-15T06:36:40
oeisdata/seq/A363/A363638.seq
dc9f50fdc91a530b6cc51812cbb5324c
A363639
Expansion of Sum_{k>0} (1/(1 - k*x^k)^3 - 1).
[ "3", "12", "19", "51", "36", "180", "57", "405", "352", "918", "111", "3990", "144", "5064", "6534", "15945", "222", "51462", "267", "99354", "82478", "160812", "369", "808490", "66051", "861630", "1090342", "2593614", "552", "8966414", "621", "13039761", "13831470", "22415778", "3166218", "114011229", "852", "110103540", "167426822" ]
[ "nonn" ]
14
1
1
[ "A338662", "A362683", "A363628", "A363639", "A363640", "A363642", "A363643", "A363644", "A363647" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-17T00:59:30
oeisdata/seq/A363/A363639.seq
6861693163c41ba1f3fee776505eaf28
A363640
Expansion of Sum_{k>0} (1/(1 - k*x^k)^4 - 1).
[ "4", "18", "32", "91", "76", "358", "148", "917", "796", "2368", "408", "10354", "612", "16586", "16984", "52873", "1208", "180408", "1616", "374934", "271408", "749070", "2692", "3350370", "178376", "4592968", "4349008", "13197802", "5076", "45402484", "6108", "74470417", "64515400", "149432876", "10324768", "652324677", "10028" ]
[ "nonn" ]
13
1
1
[ "A116963", "A338662", "A362683", "A363639", "A363640", "A363648" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-17T00:59:20
oeisdata/seq/A363/A363640.seq
b25e963bdb6ac477108f0503f9434f80
A363641
Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^2.
[ "0", "1", "2", "4", "4", "10", "6", "20", "14", "42", "10", "127", "12", "206", "132", "512", "16", "1459", "18", "2655", "1492", "5142", "22", "17795", "524", "24602", "17540", "59567", "28", "177776", "30", "274656", "196884", "524322", "20156", "1901506", "36", "2359334", "2125828", "5682323", "40", "17453224", "42", "24641943", "22948512", "46137390", "46" ]
[ "nonn" ]
13
1
3
[ "A167531", "A362683", "A363641", "A363649" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:20:06
oeisdata/seq/A363/A363641.seq
9c4f0d7bc7fa7c4e1bc6ab76e5438fea
A363642
Expansion of Sum_{k>0} x^k/(1 - k*x^k)^3.
[ "1", "4", "7", "17", "16", "55", "29", "129", "100", "311", "67", "1135", "92", "1919", "1486", "5409", "154", "17038", "191", "33491", "20938", "67871", "277", "262861", "9701", "373127", "296110", "978727", "436", "3134821", "497", "5051969", "3898522", "10027655", "474146", "39352069", "704", "49808159", "48362926", "127403221", "862", "411286429", "947" ]
[ "nonn" ]
16
1
2
[ "A007437", "A167531", "A363639", "A363642", "A363643", "A363644", "A363645", "A363650" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:14
oeisdata/seq/A363/A363642.seq
d1c3803271593b493f2d73dc6fe89e45
A363643
Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^3.
[ "0", "1", "3", "7", "10", "22", "21", "53", "45", "126", "55", "373", "78", "764", "390", "2009", "136", "5995", "171", "12501", "5334", "28392", "253", "92353", "1550", "160070", "79110", "394913", "406", "1167406", "465", "2081649", "1083126", "4457010", "69650", "14534659", "666", "22414016", "13818246", "53200481", "820", "158661826", "903" ]
[ "nonn" ]
13
1
3
[ "A363639", "A363642", "A363643", "A363644", "A363651" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:17
oeisdata/seq/A363/A363643.seq
69623e0a3d577f7cad408b54eed75b8c
A363644
Expansion of Sum_{k>0} x^(3*k)/(1 - k*x^k)^3.
[ "0", "0", "1", "3", "6", "11", "15", "27", "29", "60", "45", "145", "66", "318", "146", "789", "120", "2199", "153", "4890", "1406", "11730", "231", "34175", "426", "67884", "20738", "163956", "378", "453341", "435", "882153", "295742", "1966608", "10230", "5656484", "630", "10027674", "3897938", "23069916", "780", "63648517", "861", "113050536" ]
[ "nonn" ]
13
1
4
[ "A363610", "A363639", "A363642", "A363643", "A363644", "A363652" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:21
oeisdata/seq/A363/A363644.seq
a1afb5845f468966414bab28b6a7206d
A363645
Expansion of Sum_{k>0} x^k/(1 - k*x^k)^4.
[ "1", "5", "11", "29", "36", "109", "85", "297", "256", "801", "287", "2881", "456", "5965", "3766", "17489", "970", "57385", "1331", "125681", "63498", "294933", "2301", "1072865", "24801", "1867009", "1087030", "4942561", "4496", "15697761", "5457", "28721057", "16895770", "63511593", "1404306", "225177013", "9140", "348661477" ]
[ "nonn" ]
11
1
2
[ "A059358", "A167531", "A363642", "A363645" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:24
oeisdata/seq/A363/A363645.seq
d1bd347b84e73b16b2c8439e7c980774
A363646
Expansion of Sum_{k>0} (1/(1 - (k*x)^k)^2 - 1).
[ "2", "11", "58", "565", "6256", "95762", "1647094", "33752329", "774919720", "20029303030", "570623341234", "17838801038274", "605750213184520", "22226048320465666", "875787902918124708", "36894332593824661521", "1654480523772673528372", "78693266840741507386757" ]
[ "nonn" ]
14
1
1
[ "A007503", "A023887", "A338663", "A362683", "A363646", "A363647", "A363648" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-17T00:59:24
oeisdata/seq/A363/A363646.seq
47a7d04e24691fc585f987319a61c82a
A363647
Expansion of Sum_{k>0} (1/(1 - (k*x)^k)^3 - 1).
[ "3", "18", "91", "879", "9396", "145010", "2470665", "50728749", "1162458352", "30058615320", "855935011911", "26761537897338", "908625319776864", "33340089815701086", "1313681976619686558", "55341921135416377497", "2481720785659010292702", "118040125809311823596960" ]
[ "nonn" ]
13
1
1
[ "A023887", "A338663", "A363639", "A363646", "A363647", "A363648" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-17T00:59:13
oeisdata/seq/A363/A363647.seq
4a4e28f5fe2e3d03a5b94876a0270954
A363648
Expansion of Sum_{k>0} (1/(1 - (k*x)^k)^4 - 1).
[ "4", "26", "128", "1219", "12556", "195278", "3294292", "67773349", "1550075836", "40097713880", "1141246682808", "35686524105658", "1211500426369572", "44454809534927314", "1751576172678539608", "73789791194939982793", "3308961047545347057848", "157387135278770854655312" ]
[ "nonn" ]
13
1
1
[ "A023887", "A338663", "A363640", "A363646", "A363647", "A363648" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-17T00:59:17
oeisdata/seq/A363/A363648.seq
694fa8a5e9afaf750dff57fce6bb8764
A363649
Expansion of Sum_{k>0} x^(2*k)/(1 - (k*x)^k)^2.
[ "0", "1", "2", "4", "4", "14", "6", "56", "62", "266", "10", "3991", "12", "6158", "84996", "225296", "16", "2881607", "18", "96995583", "87740548", "2621462", "22", "30762215703", "122070312524", "50331674", "84457666628", "8631957089039", "28", "885639790229244", "30", "2814753793638432", "76826598191124" ]
[ "nonn" ]
13
1
3
[ "A359112", "A363641", "A363646", "A363649" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:26
oeisdata/seq/A363/A363649.seq
3ccf51eb4f170c73e5ecb6862d3ef8f2
A363650
Expansion of Sum_{k>0} x^k/(1 - (k*x)^k)^3.
[ "1", "4", "7", "23", "16", "199", "29", "1445", "4420", "13271", "67", "751597", "92", "2585423", "66565486", "218693769", "154", "14527231822", "191", "399614708821", "4080186211018", "856004218103", "277", "2754664372347481", "1430511474609701", "908626846503767", "900580521111136750", "5626675967703843613", "436" ]
[ "nonn" ]
13
1
2
[ "A007437", "A363642", "A363647", "A363650", "A363651", "A363652" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:29
oeisdata/seq/A363/A363650.seq
a014bceefda484f80914d981180e5e87
A363651
Expansion of Sum_{k>0} x^(2*k)/(1 - (k*x)^k)^3.
[ "0", "1", "3", "7", "10", "28", "21", "125", "117", "686", "55", "9049", "78", "21596", "206310", "508025", "136", "8701561", "171", "229315221", "303797886", "14418152", "253", "88452515089", "305175781550", "327156038", "377734977126", "27160609347425", "406", "2458857416866336", "465", "9570181420417521" ]
[ "nonn" ]
12
1
3
[ "A363643", "A363647", "A363650", "A363651", "A363652" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:32
oeisdata/seq/A363/A363651.seq
1b952d92f3434a81d3d0d682ef1ea3b8
A363652
Expansion of Sum_{k>0} x^(3*k)/(1 - (k*x)^k)^3.
[ "0", "0", "1", "3", "6", "11", "15", "33", "29", "132", "45", "777", "66", "3918", "4466", "22377", "120", "311655", "153", "992586", "7971806", "2949330", "231", "483657349", "58594026", "69206316", "10847774018", "64754136132", "378", "696335917637", "435", "23096840946129", "12709329142142", "32212255248", "1434580813047030" ]
[ "nonn" ]
12
1
4
[ "A363644", "A363647", "A363650", "A363651", "A363652" ]
null
Seiichi Manyama, Jun 13 2023
2023-07-19T02:19:36
oeisdata/seq/A363/A363652.seq
4e440f3c4572cac18f45b05205ad6c6f
A363653
a(1) = 1; for n > 1, a(n) = a(n-1) - A000005(n) if a(n) strictly positive, else a(n) = a(n-1) + A000005(n).
[ "1", "3", "1", "4", "2", "6", "4", "8", "5", "1", "3", "9", "7", "3", "7", "2", "4", "10", "8", "2", "6", "2", "4", "12", "9", "5", "1", "7", "5", "13", "11", "5", "1", "5", "1", "10", "8", "4", "8", "16", "14", "6", "4", "10", "4", "8", "6", "16", "13", "7", "3", "9", "7", "15", "11", "3", "7", "3", "1", "13", "11", "7", "1", "8", "4", "12", "10", "4", "8", "16", "14", "2", "4", "8", "2", "8", "4", "12", "10", "20", "15", "11", "9", "21" ]
[ "nonn" ]
10
1
2
[ "A000005", "A005132", "A008343", "A008344", "A046901", "A063733", "A336760", "A363653" ]
null
Ctibor O. Zizka, Jun 13 2023
2023-07-06T22:05:59
oeisdata/seq/A363/A363653.seq
67c67ba6b337216fb6e8fa684a81596a
A363654
Lexicographically earliest sequence of positive integers such that the n-th pair of identical terms encloses exactly a(n) terms.
[ "1", "2", "1", "3", "2", "3", "1", "2", "4", "3", "4", "5", "3", "6", "7", "4", "3", "8", "6", "9", "7", "8", "4", "10", "3", "7", "4", "6", "8", "9", "11", "10", "12", "3", "9", "13", "7", "3", "11", "9", "14", "15", "13", "16", "17", "7", "18", "3", "19", "20", "11", "14", "9", "20", "17", "15", "19", "20", "18", "21", "11", "22", "3", "23", "24", "25", "26", "14", "17", "9", "27", "28", "29", "15", "26", "19" ]
[ "nonn" ]
32
1
2
[ "A026272", "A363654", "A363708", "A363757" ]
null
Eric Angelini and Gavin Lupo, Jun 13 2023
2023-07-25T09:14:47
oeisdata/seq/A363/A363654.seq
779ebfcd5b7bb750d341628ddc283404
A363655
a(0) = 1; for n > 0, a(n) = prime( Sum_{k=0..n-1} a(k) * a(n-k-1) ).
[ "1", "2", "7", "61", "863", "17569", "472741", "16007419", "659408567", "32231133931", "1833425773489", "119498316410171", "8810846732918257", "727089137774221667" ]
[ "nonn", "hard", "more" ]
6
0
2
[ "A000040", "A000108", "A007097", "A014342", "A093502", "A338816", "A363655" ]
null
Ilya Gutkovskiy, Jun 13 2023
2023-07-21T16:06:12
oeisdata/seq/A363/A363655.seq
a4c776a0b1f5f0eae47a270a285372f9
A363656
Number of bounded affine permutations of size n.
[ "1", "3", "13", "87", "761", "8243", "106037", "1578671", "26685361", "504770859", "10562259533", "242216304839", "6040459572681", "162750100464643", "4711225866217381", "145818462291970911", "4805369568409107809", "167982555421167341147", "6208589923091273031293", "241898639921607255506039" ]
[ "nonn" ]
30
1
2
[ "A046739", "A173018", "A363656" ]
null
Justin M. Troyka, Jun 14 2023
2023-06-14T16:46:32
oeisdata/seq/A363/A363656.seq
c61a921f1941b5733928754a51aec0de
A363657
Numbers m where A217854(m) is a record minimum.
[ "1", "4", "9", "16", "36", "100", "144", "324", "400", "576", "900", "1764", "2304", "3600", "7056", "8100", "14400", "28224", "32400", "44100", "57600", "108900", "112896", "129600", "176400", "396900", "435600", "518400", "608400", "705600", "1587600", "2822400", "5336100", "6350400", "14288400", "15681600", "17640000", "21344400" ]
[ "nonn" ]
36
1
2
[ "A000005", "A000290", "A067128", "A217854", "A224914", "A363657", "A363658" ]
null
Simon Jensen, Jun 13 2023
2023-09-29T18:32:22
oeisdata/seq/A363/A363657.seq
3f3d96016152f7a2b2aa083beee2a3e8
A363658
Positive numbers m where A217854(m) is positive and increases to a record.
[ "2", "3", "5", "6", "8", "10", "12", "18", "20", "24", "30", "40", "42", "48", "60", "72", "84", "90", "96", "108", "120", "168", "180", "240", "336", "360", "420", "480", "504", "540", "600", "630", "660", "672", "720", "840", "1080", "1260", "1440", "1680", "2160", "2520", "3360", "3780", "3960", "4200", "4320", "4620", "4680", "5040", "7560", "9240", "10080" ]
[ "nonn" ]
41
1
1
[ "A000005", "A002093", "A067128", "A217854", "A224914", "A363657", "A363658" ]
null
Simon Jensen, Jun 13 2023
2023-09-01T03:59:34
oeisdata/seq/A363/A363658.seq
b6b30bfc1fd37f16631f0e1a7feb0220
A363659
Numbers k such that the last letter of k is the same as the first letter of k+1 when written in English.
[ "0", "18", "28", "38", "79", "81", "83", "85", "97", "102", "122", "132", "142", "152", "162", "172", "182", "192", "208", "228", "238", "248", "258", "268", "278", "288", "298", "308", "328", "338", "348", "358", "368", "378", "388", "398", "799", "801", "803", "805", "809", "812", "821", "823", "825", "829", "831", "833", "835", "839", "841", "843", "845", "849" ]
[ "nonn", "word" ]
11
1
2
null
null
Sean A. Irvine, Jun 14 2023
2023-06-14T10:33:58
oeisdata/seq/A363/A363659.seq
5c2cff50828a081b2c62b31d53ececd0
A363660
a(n) = Sum_{d|n} binomial(d+n,n).
[ "2", "9", "24", "90", "258", "1043", "3440", "13419", "48850", "187836", "705444", "2725099", "10400614", "40233015", "155133856", "601820876", "2333606238", "9079958260", "35345263820", "137876637843", "538259060526", "2104292500739", "8233430727624", "32248866496625", "126410606580284" ]
[ "nonn" ]
17
1
1
[ "A000984", "A007503", "A116963", "A134758", "A343548", "A343549", "A363628", "A363660", "A363661" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-17T00:58:25
oeisdata/seq/A363/A363660.seq
0c1364443de81793dbc682205e8410fd
A363661
a(n) = Sum_{d|n} (n/d)^d * binomial(d+n,n).
[ "2", "12", "32", "150", "282", "1890", "3488", "21582", "54650", "282612", "705564", "4072224", "10400782", "55006530", "158987232", "790611350", "2333606526", "11573213196", "35345264180", "168673694070", "540848064614", "2500462200182", "8233430728152", "37445946291600", "126411051769652" ]
[ "nonn" ]
18
1
1
[ "A055225", "A362683", "A363639", "A363640", "A363660", "A363661", "A363662", "A363663" ]
null
Seiichi Manyama, Jun 14 2023
2023-11-23T20:21:11
oeisdata/seq/A363/A363661.seq
63166cb9d060c01c0fcb76c0660f1088
A363662
a(n) = Sum_{d|n} (n/d)^n * binomial(d+n,n).
[ "2", "18", "128", "1590", "19002", "353304", "6591776", "154083654", "3878583770", "110647791078", "3423740752764", "116116072618104", "4240251502692142", "166761491097360240", "7006327371058071648", "313637735782416564806", "14890324713956395361406", "747610406539465959084870" ]
[ "nonn" ]
12
1
1
[ "A023887", "A363646", "A363647", "A363648", "A363660", "A363661", "A363662" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:02:13
oeisdata/seq/A363/A363662.seq
2272a477dbd2f196b80963c77c9f2a9b
A363663
a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-1,n).
[ "1", "4", "11", "46", "127", "596", "1717", "7792", "24806", "108450", "352717", "1563914", "5200301", "22539046", "77876117", "331982444", "1166803111", "4945693769", "17672631901", "74053888812", "269344740908", "1118110015874", "4116715363801", "16984153623296", "63205318063252", "259049084680612" ]
[ "nonn" ]
14
1
2
[ "A167531", "A343548", "A363642", "A363645", "A363661", "A363663", "A363664" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:02:17
oeisdata/seq/A363/A363663.seq
0dc9085b5561d49b186aa4e03b08df31
A363664
a(n) = Sum_{d|n} (n/d)^(n-n/d) * binomial(d+n-1,n).
[ "1", "4", "11", "56", "127", "1100", "1717", "19300", "64406", "383010", "352717", "23214660", "5200301", "191172406", "3465549077", "20859527460", "1166803111", "1010698826825", "17672631901", "102589250081802", "286539905316908", "75260204476154", "4116715363801", "548610025890719156" ]
[ "nonn" ]
15
1
2
[ "A342628", "A343548", "A359112", "A363650", "A363662", "A363663", "A363664", "A363667" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:02:10
oeisdata/seq/A363/A363664.seq
9948c6f46f9e276f0ece1ba4eac3b438
A363665
Starting with a(1) = 1, the lexicographically earliest sequence of integers on a square spiral such that every number equals the sum of its eight adjacent neighbors.
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "-2", "0", "0", "1", "-2", "0", "0", "0", "-1", "0", "0", "0", "-2", "2", "0", "0", "-1", "2", "-3", "0", "0", "3", "-2", "2", "-3", "0", "0", "3", "-1", "-1", "1", "0", "0", "1", "0", "0", "-5", "8", "0", "0", "-5", "4", "0", "4", "-7", "0", "0", "6", "-6", "4", "-4", "8", "-7", "0", "0", "2", "-2", "4", "-4", "0", "7", "0", "0", "-8", "6", "3", "-8", "10", "-15", "16", "0", "0", "-9", "6", "-5", "7", "-8", "13" ]
[ "sign" ]
17
1
12
[ "A355270", "A358151", "A358337", "A361724", "A363665" ]
null
Scott R. Shannon, Jun 14 2023
2023-07-07T14:58:16
oeisdata/seq/A363/A363665.seq
7bd1c7a49aeb67365dcc25090c7c4b09
A363666
a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-2,n-1).
[ "1", "3", "7", "29", "71", "355", "925", "4425", "13276", "60111", "184757", "856357", "2704157", "12137147", "40367461", "176999505", "601080391", "2616894901", "9075135301", "38884056181", "138014377810", "583674491643", "2104098963721", "8823912454489", "32247616479976", "133998376789707" ]
[ "nonn" ]
12
1
2
[ "A167531", "A332508", "A363642", "A363645", "A363663", "A363666", "A363667" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:02:06
oeisdata/seq/A363/A363666.seq
e86b4ce179da0f84351373398e655d1d
A363667
a(n) = Sum_{d|n} (n/d)^(n-n/d) * binomial(d+n-2,n-1).
[ "1", "3", "7", "37", "71", "751", "925", "13161", "45676", "262911", "184757", "18014557", "2704157", "133062875", "2838201061", "16907954129", "601080391", "830283170617", "9075135301", "87074953375981", "246003195539410", "53321730394923", "2104098963721", "479275771000215865", "1952680410445479976" ]
[ "nonn" ]
11
1
2
[ "A342628", "A359112", "A363650", "A363664", "A363666", "A363667" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:02:01
oeisdata/seq/A363/A363667.seq
2af3ff667cf86d44a67719ed22c90f4c
A363668
a(n) = Sum_{d|n} (n/d)^d * binomial(d+n-1,d).
[ "1", "7", "19", "91", "151", "1135", "1765", "12355", "28846", "157917", "352837", "2280955", "5200469", "29986201", "80469589", "427061795", "1166803399", "6211188028", "17672632261", "89483074521", "271071666724", "1316291647997", "4116715364329", "19595444140771", "63205674328876", "292318539358879" ]
[ "nonn" ]
12
1
2
[ "A055225", "A343549", "A362683", "A363639", "A363640", "A363668", "A363669" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:01:56
oeisdata/seq/A363/A363668.seq
bb6d9f5081439a16a2ab50e73b0c2524
A363669
a(n) = Sum_{d|n} (n/d)^n * binomial(d+n-1,d).
[ "1", "11", "91", "1219", "15751", "299291", "5766517", "136667939", "3490056406", "100539251801", "3138428729437", "107169878769043", "3937376390899589", "155639310270607349", "6568429274592664981", "295186202455912472867", "14063084452068891794119", "708261127356256620907496" ]
[ "nonn" ]
11
1
2
[ "A343549", "A363646", "A363647", "A363648", "A363668", "A363669" ]
null
Seiichi Manyama, Jun 14 2023
2023-07-12T01:01:53
oeisdata/seq/A363/A363669.seq
b8c91f3c4296091bf189b3813b1c414b
A363670
Natural numbers k divisible by all natural numbers < log(k) + log(1 + log(k)).
[ "1", "2", "3", "4", "6", "12", "24", "60", "120", "420", "840", "2520", "5040", "27720", "360360", "720720", "1441440", "232792560", "80313433200", "144403552893600", "288807105787200", "5342931457063200", "10685862914126400", "16028794371189600", "164249358725037825439200", "328498717450075650878400", "492748076175113476317600", "656997434900151301756800" ]
[ "nonn" ]
13
1
2
[ "A003418", "A363670" ]
null
Hal M. Switkay, Jun 14 2023
2023-06-16T09:00:29
oeisdata/seq/A363/A363670.seq
bd660114e0cf9b745cc3dc808bb9acb2
A363671
Triangular array: row n lists the numbers k such that prime(n+2)-2*k is a prime.
[ "1", "1", "2", "2", "3", "4", "1", "3", "4", "5", "2", "3", "5", "6", "7", "1", "3", "4", "6", "7", "8", "2", "3", "5", "6", "8", "9", "10", "3", "5", "6", "8", "9", "11", "12", "13", "1", "4", "6", "7", "9", "10", "12", "13", "14", "3", "4", "7", "9", "10", "12", "13", "15", "16", "17", "2", "5", "6", "9", "11", "12", "14", "15", "17", "18", "19", "1", "3", "6", "7", "10", "12", "13", "15", "16", "18", "19" ]
[ "nonn", "tabl" ]
11
1
3
[ "A000040", "A028334", "A067076", "A363671", "A363672" ]
null
Clark Kimberling, Jun 15 2023
2023-08-02T11:48:22
oeisdata/seq/A363/A363671.seq
78c6039d6f2f371d9080b1c7bcd327a8
A363672
Triangular array: row n lists the primes indexed by the array in A363671.
[ "2", "2", "3", "3", "5", "7", "2", "5", "7", "11", "3", "5", "11", "13", "17", "2", "5", "7", "13", "17", "19", "3", "5", "11", "13", "19", "23", "29", "5", "11", "13", "19", "23", "31", "37", "41", "2", "7", "13", "17", "23", "29", "37", "41", "43", "5", "7", "17", "23", "29", "37", "41", "47", "53", "59", "3", "11", "13", "23", "31", "37", "43", "47", "59", "61", "67", "2", "5", "13", "17", "29" ]
[ "nonn", "tabl" ]
10
1
1
[ "A000040", "A087478", "A363671", "A363672" ]
null
Clark Kimberling, Jun 15 2023
2023-07-23T22:27:28
oeisdata/seq/A363/A363672.seq
b947f98caac551d1b0724d1c5175fcec
A363673
a(n) is the least prime factor (> 3) in the factorization of 2^(2*prime(n))-1.
[ "5", "7", "11", "43", "23", "2731", "43691", "174763", "47", "59", "715827883", "223", "83", "431", "283", "107", "2833", "768614336404564651", "7327657", "228479", "439", "2687", "167", "179", "971", "7432339208719", "2550183799", "643", "104124649", "227", "56713727820156410577229101238628035243", "263", "1097", "4506937", "1193", "18121", "15073", "150287" ]
[ "nonn" ]
12
1
1
[ "A152099", "A363673" ]
null
Alain Rocchelli, Jun 14 2023
2023-06-26T14:48:00
oeisdata/seq/A363/A363673.seq
9cf9b731df6f076901fc56b7e3adea39
A363674
T(n,k) is the decimal equivalent of the n-bit inverted Gray code for k; triangle T(n,k), n>=0, 0<=k<=2^n-1, read by rows.
[ "0", "1", "0", "3", "2", "0", "1", "7", "6", "4", "5", "1", "0", "2", "3", "15", "14", "12", "13", "9", "8", "10", "11", "3", "2", "0", "1", "5", "4", "6", "7", "31", "30", "28", "29", "25", "24", "26", "27", "19", "18", "16", "17", "21", "20", "22", "23", "7", "6", "4", "5", "1", "0", "2", "3", "11", "10", "8", "9", "13", "12", "14", "15", "63", "62", "60", "61", "57", "56", "58", "59", "51", "50", "48" ]
[ "nonn", "tabf", "look" ]
40
0
4
[ "A000120", "A000225", "A000918", "A000975", "A003188", "A006516", "A028399", "A063524", "A097072", "A236840", "A329278", "A331105", "A362160", "A363674" ]
null
Alois P. Heinz, Jun 14 2023
2023-07-14T11:51:49
oeisdata/seq/A363/A363674.seq
270a9bb151205717fba7037e5ef5982f
A363675
Numbers k such that the least common multiple of the degrees of the irreducible characters of S_k equals |S_k| = k!.
[ "0", "1", "6", "10", "21", "36", "66", "105", "120", "136", "190", "210", "276", "325", "465", "496", "561", "630", "666", "741", "780", "990", "1081", "1176", "1225", "1540", "1596", "1830", "2080", "2145", "2346", "2556", "2926", "3081", "3160", "3240", "3486", "3570", "3916", "4005", "4186", "4560", "4656", "4950", "5050", "5356", "5460", "5886", "6105" ]
[ "nonn" ]
61
1
3
[ "A000142", "A000217", "A010054", "A033687", "A175595", "A260682", "A267137", "A363675", "A363676", "A363701" ]
null
Diego Martin Duro, Jun 14 2023
2023-10-18T09:08:06
oeisdata/seq/A363/A363675.seq
f017631fb1f27f8ebf56d341dc86553c
A363676
Numbers k such that the least common multiple of the degrees of the irreducible characters of A_k equals |A_k| = k!/2.
[ "0", "1", "2", "5", "6", "8", "10", "12", "17", "21", "30", "36", "57", "66", "80", "105", "120", "122", "136", "190", "192", "210", "212", "233", "276", "302", "325", "380", "408", "465", "496", "530", "561", "597", "630", "632", "666", "705", "741", "780", "782", "822", "905", "990", "992", "1081", "1130", "1176", "1225", "1433", "1540", "1542", "1596", "1772" ]
[ "nonn" ]
45
1
3
[ "A000217", "A010054", "A175595", "A260682", "A267137", "A363675", "A363676", "A363701" ]
null
Diego Martin Duro, Jun 14 2023
2023-10-18T09:06:35
oeisdata/seq/A363/A363676.seq
e10e0fc4f79bcadb42e12840ec19ef10
A363677
The series limit of Sum_{k>=2} cos(log k)/(k*log k).
[ "2", "5", "3", "9", "5", "5", "3", "6", "4", "8", "2", "1", "1", "7", "3", "4", "7", "5", "8", "9", "1", "0", "9", "7" ]
[ "cons", "nonn", "more" ]
24
0
1
null
null
R. J. Mathar, Jun 14 2023
2023-06-17T13:11:01
oeisdata/seq/A363/A363677.seq
a75162cf5950765c6f106135364700b8
A363678
Start with the list of positive integers. For each m = 1, 2, 3, ..., insert a copy of the number m after each of the next m-1 terms.
[ "1", "2", "3", "2", "3", "4", "3", "4", "5", "4", "5", "6", "5", "6", "4", "6", "5", "6", "7", "6", "7", "5", "7", "6", "7", "8", "7", "8", "9", "8", "9", "7", "9", "8", "9", "10", "9", "10", "8", "10", "9", "10", "7", "10", "9", "10", "8", "10", "9", "10", "11", "10", "11", "9", "11", "10", "11", "8", "11", "12", "11", "12", "8", "12", "11", "12", "13", "12", "13", "11", "13", "12", "13", "14", "13", "14", "12", "14", "13", "14", "11", "14", "13", "14" ]
[ "nonn" ]
48
1
2
null
null
Ali Sada, Jul 09 2023
2025-05-11T11:44:10
oeisdata/seq/A363/A363678.seq
85d459dd89621661f0ad7d0ce7f228b2
A363679
Decimal expansion of the sum of the reciprocals of triangular polygorials A006472.
[ "2", "3", "9", "4", "8", "3", "3", "0", "9", "9", "2", "7", "3", "4", "0", "4", "7", "1", "6", "5", "2", "2", "6", "3", "2", "6", "3", "6", "4", "3", "6", "3", "7", "3", "1", "5", "1", "9", "6", "8", "6", "3", "7", "0", "0", "7", "0", "9", "1", "3", "6", "2", "4", "4", "4", "7", "2", "6", "7", "9", "7", "5", "6", "3", "8", "5", "7", "2", "9", "5", "5", "5", "9", "4", "8", "3", "3", "3", "3", "4", "6", "4", "0", "5", "2", "4", "5", "5", "9", "4", "9", "9", "7", "1", "2", "3", "1", "5", "0", "7", "8", "9", "2", "5", "2", "2", "3", "6", "9", "3", "1", "1", "0", "3", "7", "8", "4", "9", "6", "1" ]
[ "nonn", "cons" ]
19
1
1
[ "A001113", "A006472", "A070910", "A363679", "A365077" ]
null
Kelvin Voskuijl, Aug 17 2023
2023-08-22T11:58:12
oeisdata/seq/A363/A363679.seq
8e657f2786577513bdbfa772f782a299
A363680
Number of iterations of phi(x) at n needed to reach a cube.
[ "0", "1", "2", "2", "3", "2", "3", "0", "3", "3", "4", "3", "4", "3", "1", "1", "2", "3", "4", "1", "4", "4", "5", "1", "2", "4", "0", "4", "5", "1", "2", "2", "2", "2", "2", "4", "5", "4", "2", "2", "3", "4", "5", "2", "2", "5", "6", "2", "5", "2", "3", "2", "3", "4", "3", "2", "5", "5", "6", "2", "3", "2", "5", "0", "3", "2", "3", "3", "3", "2", "3", "2", "3", "5", "3", "5", "3", "2", "3", "3", "5", "3", "4", "2", "1", "5", "3" ]
[ "nonn" ]
12
1
3
[ "A000010", "A003434", "A363612", "A363680" ]
null
Darío Clavijo, Jun 14 2023
2023-06-15T20:06:35
oeisdata/seq/A363/A363680.seq
b95c75e5371a09e819a10661c7d120d7
A363681
Sphenic numbers sandwiched between two squarefree semiprimes.
[ "186", "266", "322", "470", "518", "534", "582", "590", "670", "754", "790", "814", "894", "994", "1146", "1158", "1166", "1338", "1390", "1562", "1686", "1798", "1842", "1958", "2118", "2158", "2230", "2318", "2454", "2482", "2514", "2570", "2630", "2758", "2786", "2922", "2930", "2994", "3154", "3206", "3262", "3278", "3378", "3454", "3522", "3562", "3714", "3786", "3830", "3838", "3962", "3982" ]
[ "nonn" ]
5
1
1
[ "A006881", "A007304", "A362811", "A363681" ]
null
Tanya Khovanova and Massimo Kofler, Jun 14 2023
2023-07-22T17:03:58
oeisdata/seq/A363/A363681.seq
082eff91f711bfb81f66b5efa6f8a838
A363682
Number of plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) with n edges.
[ "1", "1", "1", "2", "5", "12", "32", "93", "279", "872", "2830", "9433", "32223", "112527", "400370", "1448520", "5320023", "19802827", "74612164", "284238390", "1093757436", "4247742956", "16636921148", "65671960544", "261111950308", "1045172796381", "4209807155949", "17055625810984", "69476952146529", "284467866640048" ]
[ "nonn" ]
31
1
4
[ "A001181", "A117106", "A151335", "A296419", "A363682" ]
null
Éric Fusy, Jun 16 2023
2023-08-18T15:59:46
oeisdata/seq/A363/A363682.seq
54b389ea9208518ad573e030691bb9f0
A363683
Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the least e > 0 such that n^e and k^e have the same initial digit, or -1 if no such e exists.
[ "1", "4", "4", "9", "1", "9", "2", "17", "17", "2", "3", "7", "1", "7", "3", "4", "5", "8", "8", "5", "4", "5", "4", "9", "1", "9", "4", "5", "8", "2", "3", "11", "11", "3", "2", "8", "16", "5", "11", "6", "1", "6", "11", "5", "16", "1", "17", "7", "4", "9", "9", "4", "7", "17", "1", "1", "4", "17", "10", "6", "1", "6", "10", "17", "4", "1", "1", "4", "9", "14", "5", "15", "15", "5", "14", "9", "4", "1" ]
[ "nonn", "base", "tabl" ]
5
1
2
[ "A000030", "A073601", "A088995", "A098174", "A359698", "A363683" ]
null
Rémy Sigrist, Jun 15 2023
2023-06-17T14:22:53
oeisdata/seq/A363/A363683.seq
c33ac2e325395f215995c81a8f637a2b
A363684
Decimal expansion of Product_{k>=1} Gamma(2k/(2k-1)) / Gamma(1+1/(2k)).
[ "1", "0", "6", "2", "1", "5", "0", "9", "0", "5", "5", "7", "1", "0", "5", "7", "2", "8", "0", "6", "9", "6", "8", "3", "7", "3", "6", "2", "9", "3", "8", "0", "9", "9", "9", "0", "4", "2", "5", "2", "0", "7", "9", "5", "5", "2", "0", "0", "4", "5", "6", "9", "3", "3", "3", "4", "0", "7", "9", "8", "7", "0", "0", "9", "0", "5", "3", "7", "9", "8", "9", "3", "7", "0", "7", "7", "1", "4", "0", "8", "2", "9", "1", "9", "3", "6", "1", "8", "2", "5", "3", "6", "8", "6", "6", "9", "3", "1", "7", "7", "6", "0", "2", "1", "9", "7" ]
[ "cons", "nonn" ]
18
1
3
[ "A303670", "A363684" ]
null
R. J. Mathar, Jun 15 2023
2024-06-11T12:47:05
oeisdata/seq/A363/A363684.seq
0aa24e9333cf8789edd3eceab6a8eefe
A363685
Irregular triangle read by rows: T(n,k) is the number of descending plane partitions of order n with the sum of the parts equal to k.
[ "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "2", "2", "3", "2", "4", "3", "4", "3", "4", "2", "3", "2", "2", "1", "1", "0", "1", "1", "0", "1", "1", "2", "3", "4", "4", "7", "7", "10", "11", "14", "14", "18", "18", "21", "21", "23", "22", "25", "22", "23", "21", "21", "18", "18", "14", "14", "11", "10", "7", "7", "4", "4", "3", "2", "1", "1", "0", "1" ]
[ "nonn", "tabf" ]
17
1
18
[ "A005130", "A064999", "A198890", "A363685" ]
null
Ludovic Schwob, Jun 15 2023
2023-09-22T05:36:13
oeisdata/seq/A363/A363685.seq
add83a0cdc160649b8ebf2a3d3e57ddd
A363686
Irregular triangle T(n, k) read by rows which represents a predecessor number system for Collatz sequences (see Comments for precise definition).
[ "5", "3", "17", "23", "25", "11", "65", "15", "73", "59", "33", "7", "185", "43", "257", "95", "105", "219", "97", "39", "249", "363", "385", "175", "9", "123", "929", "199", "57", "171", "1025", "63", "297", "411", "481", "487", "633", "747", "129", "367", "393", "507", "1697", "583", "1849", "939", "513", "287", "233", "347", "1377", "423", "1529", "619", "3969", "815", "265", "1403", "1441", "1479", "1593", "683", "4097" ]
[ "nonn", "tabf" ]
106
1
1
[ "A000079", "A000265", "A052539", "A056792", "A283507", "A339694", "A363686" ]
null
Paul Conradi, Jun 15 2023
2025-02-16T08:34:05
oeisdata/seq/A363/A363686.seq
8467cc4bd014d176d840d65d474f4cc4
A363687
Decimal expansion of Sum_{k>=1} cos(Pi* log k)/k^2.
[ "7", "9", "5", "6", "4", "0", "2", "0", "6", "7", "3", "5", "6", "7", "7", "5", "1", "7", "4", "3", "0", "6", "2", "8", "3", "2", "8", "4", "9", "8", "7", "6", "0", "8", "1", "2", "0", "9", "9", "0", "9", "6", "2", "6", "9", "7", "4", "8", "8", "7", "5", "4", "8", "3", "8", "2", "6", "1", "7", "1", "5", "7", "6", "1", "0", "8", "7", "4", "2", "8", "5", "9", "4", "1", "6", "8", "1", "8", "1", "8", "1", "0", "1", "4", "2", "9", "8", "3", "1", "3", "5", "2", "4", "2", "4", "1", "6", "1", "8", "6", "4", "1", "3", "8", "3" ]
[ "cons", "nonn" ]
16
0
1
null
null
R. J. Mathar, Jun 15 2023
2025-03-27T05:44:11
oeisdata/seq/A363/A363687.seq
7a1b13b632e4425b663b85d6080fdb0d
A363688
Decimal expansion of the real part of zeta(1+Pi*i), where i=sqrt(-1).
[ "6", "3", "4", "7", "0", "4", "6", "9", "7", "3", "5", "4", "2", "7", "0", "1", "6", "2", "5", "9", "0", "3", "4", "6", "9", "3", "9", "2", "4", "5", "7", "4", "5", "2", "5", "7", "7", "5", "5", "5", "8", "0", "9", "1", "2", "8", "1", "5", "5", "9", "4", "5", "9", "4", "8", "9", "9", "3", "5", "2", "4", "2", "5", "1", "3", "6", "9", "4", "9", "5", "0", "9", "2", "9", "9", "3", "9", "8", "5", "1", "5", "1", "0", "2", "5", "3", "4", "4", "7", "8", "9", "8", "7", "1", "0", "1", "7", "7", "8", "6", "2", "4", "7", "5", "6" ]
[ "cons", "nonn" ]
9
0
1
[ "A363687", "A363688" ]
null
R. J. Mathar, Jun 15 2023
2023-06-16T05:10:44
oeisdata/seq/A363/A363688.seq
eeb5637cd96045804320d2203906b40f
A363689
Number of alternating sign matrices of size n which are indecomposable by direct and skew sums.
[ "1", "1", "0", "1", "16", "257", "5636", "187432", "9956054", "867875816", "125861715682", "30575624363575", "12486657463326416", "8588874417105963246", "9960958211434474577452", "19489076635898035234022220", "64349049302453152886635937502", "358611453994361731825817399132622", "3373425033361375072576454177693810076" ]
[ "nonn" ]
13
0
5
[ "A005130", "A231498", "A359856", "A363689" ]
null
Ludovic Schwob, Jun 15 2023
2023-07-24T15:09:40
oeisdata/seq/A363/A363689.seq
09c05cf182c92cdcf21c81611b5c16f0
A363690
Numbers k such that A246600(k) = 2.
[ "3", "5", "6", "7", "9", "10", "11", "12", "13", "14", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "28", "29", "31", "33", "34", "35", "36", "37", "38", "40", "41", "42", "43", "44", "46", "47", "48", "49", "50", "52", "53", "56", "57", "58", "59", "61", "62", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "76", "77", "79", "80", "81", "82", "83", "84", "86", "88" ]
[ "nonn", "base", "easy" ]
13
1
1
[ "A000079", "A006519", "A080943", "A100484", "A246600", "A363690", "A363691" ]
null
Amiram Eldar, Jun 16 2023
2023-06-21T06:46:20
oeisdata/seq/A363/A363690.seq
c160203974a3789db131c66898de7242
A363691
Odd numbers k such that A246600(k) = 2.
[ "3", "5", "7", "9", "11", "13", "17", "19", "21", "23", "25", "29", "31", "33", "35", "37", "41", "43", "47", "49", "53", "57", "59", "61", "65", "67", "69", "71", "73", "77", "79", "81", "83", "89", "91", "93", "97", "101", "103", "105", "107", "109", "113", "115", "117", "121", "127", "129", "131", "133", "137", "139", "141", "145", "149", "151", "155", "157", "161", "163", "167" ]
[ "nonn", "base", "easy" ]
13
1
1
[ "A001248", "A065091", "A246600", "A363690", "A363691" ]
null
Amiram Eldar, Jun 16 2023
2023-06-21T06:47:18
oeisdata/seq/A363/A363691.seq
37954d0b206e68c98cf8ab949b141bb0
A363692
Terms of A363690 with a record number of divisors.
[ "3", "6", "12", "24", "36", "48", "72", "144", "168", "288", "336", "420", "840", "1680", "3360", "6720", "7560", "15120", "30240", "60480", "95760", "120960", "176400", "191520", "257040", "352800", "383040", "514080", "1028160", "1681680", "2056320", "2998800", "3112200", "5525520", "5997600", "6224400", "8353800", "12448800", "16216200" ]
[ "nonn", "base" ]
14
1
1
[ "A000005", "A359082", "A359083", "A361937", "A363690", "A363692", "A363693" ]
null
Amiram Eldar, Jun 16 2023
2023-07-13T12:49:24
oeisdata/seq/A363/A363692.seq
5a1116e219b2e28b289b8e59986c7950
A363693
Terms of A363691 with a record number of divisors.
[ "3", "9", "21", "81", "105", "225", "945", "5265", "5985", "11025", "16065", "36225", "89505", "105105", "187425", "345345", "389025", "1044225", "2027025", "4189185", "6185025", "20307105", "27776385", "76039425", "107972865", "286711425", "402026625", "1853445825", "2440353825", "3807428625", "5106886785", "9449834625" ]
[ "nonn", "base" ]
5
1
1
[ "A000005", "A359082", "A359083", "A361937", "A363691", "A363692", "A363693" ]
null
Amiram Eldar, Jun 16 2023
2023-06-18T02:02:30
oeisdata/seq/A363/A363693.seq
895bb72837efbe95170b95d4e3204585
A363694
Number of edges in the prime (Gruenberg-Kegel) graph of the symmetric group, S_n, on n elements.
[ "0", "0", "0", "0", "1", "1", "2", "3", "4", "5", "5", "6", "7", "8", "9", "11", "11", "13", "14", "16", "17", "19", "19", "22", "23", "25", "25", "27", "27", "30", "31", "33", "34", "37", "37", "41", "41", "42", "43", "46", "46", "50", "51", "54", "55", "58", "58", "63", "64", "68", "68", "71", "71", "76", "77", "80", "80", "83", "83", "89", "90", "92", "93", "98", "98", "104", "104", "106", "107", "112", "112", "118", "119" ]
[ "nonn" ]
19
1
7
null
null
Lixin Zheng, Jun 15 2023
2023-08-06T01:52:48
oeisdata/seq/A363/A363694.seq
b3cc32d6612956e9e56c04fbbc086462
A363695
Expansion of Sum_{k>0} (1/(1-x^k)^5 - 1).
[ "5", "20", "40", "90", "131", "265", "335", "585", "755", "1147", "1370", "2155", "2385", "3410", "4042", "5430", "5990", "8295", "8860", "11843", "13020", "16335", "17555", "23125", "23882", "29805", "32220", "39440", "40925", "51644", "52365", "64335", "67450", "79820", "82712", "101575", "101275", "120805", "125830", "148089", "149000", "179490" ]
[ "nonn", "easy" ]
19
1
1
[ "A007503", "A073570", "A116963", "A363605", "A363608", "A363628", "A363695", "A363696" ]
null
Seiichi Manyama, Jun 16 2023
2023-07-05T01:45:16
oeisdata/seq/A363/A363695.seq
cdc2fb38692fba69b1cfb02aa7c0b02e
A363696
Expansion of Sum_{k>0} (1/(1-x^k)^6 - 1).
[ "6", "27", "62", "153", "258", "545", "798", "1440", "2064", "3282", "4374", "6859", "8574", "12447", "15818", "21789", "26340", "36196", "42510", "56538", "66634", "85125", "98286", "126901", "142764", "178506", "203440", "249909", "278262", "343936", "376998", "457686", "506372", "602118", "659058", "791908", "850674", "1005129", "1094638" ]
[ "nonn", "easy" ]
18
1
1
[ "A007503", "A101289", "A116963", "A363606", "A363628", "A363695", "A363696" ]
null
Seiichi Manyama, Jun 16 2023
2023-07-05T01:45:13
oeisdata/seq/A363/A363696.seq
bb8c724f40e8192730c5acc12acf90da
A363697
a(n) = -n! * Sum_{d|n} (-n/d)^d / d!.
[ "1", "3", "19", "47", "601", "2039", "35281", "-26881", "4898881", "-8104321", "439084801", "576132479", "80951270401", "-913158005761", "49506372115201", "-558073906790401", "6046686277632001", "79958674981785599", "2311256907767808001", "-115583806104986419201" ]
[ "sign", "easy" ]
17
1
2
[ "A132958", "A354843", "A363697", "A363698" ]
null
Seiichi Manyama, Jun 16 2023
2023-07-03T00:53:10
oeisdata/seq/A363/A363697.seq
249ef9ca2e2ba42e95479b357aa5396f
A363698
a(n) = n! * Sum_{d|n} (-1)^(d+1) * (n/d)^n / d!.
[ "1", "7", "163", "5951", "375001", "33337559", "4150656721", "675135713279", "140588337476161", "36270281280965759", "11388728893445164801", "4270306368140557557119", "1886009588552176549862401", "968696203690612910273080319" ]
[ "nonn" ]
22
1
2
[ "A132958", "A354892", "A363697", "A363698" ]
null
Seiichi Manyama, Jun 16 2023
2023-07-03T00:53:18
oeisdata/seq/A363/A363698.seq
c4d8f286803b7630d1cc5f9a6d68cf00
A363699
Radicands of pure cubic number fields of type BETA and subtype M0.
[ "2", "455", "833", "850", "1078", "1235", "1430", "1573", "3857", "4901", "6061", "6358", "6370", "8294", "8959", "9922", "11284", "12121", "12673", "12818", "14801", "17986", "18241", "20539", "21607", "22747", "23218", "26474", "27115", "29716", "30073", "31046", "32062", "32269", "33337", "36518", "37570", "38399", "38657", "38686", "39146", "40223", "41990", "42143" ]
[ "nonn" ]
76
1
1
[ "A363699", "A363717" ]
null
Daniel Constantin Mayer, Jul 09 2023
2023-07-23T02:11:07
oeisdata/seq/A363/A363699.seq
03f16e082f30b8bbd0409ee574e6e7b9
A363700
a(n) = phi(2*prime(n)+1).
[ "4", "6", "10", "8", "22", "18", "24", "24", "46", "58", "36", "40", "82", "56", "72", "106", "96", "80", "72", "120", "84", "104", "166", "178", "96", "168", "132", "168", "144", "226", "128", "262", "200", "180", "264", "200", "144", "216", "264", "346", "358", "220", "382", "252", "312", "216", "276", "296", "288", "288", "466", "478", "264", "502", "408", "480", "420", "360", "288", "562" ]
[ "nonn" ]
17
1
1
[ "A000010", "A000040", "A008331", "A037225", "A072055", "A363700" ]
null
Alain Rocchelli, Jun 16 2023
2023-06-20T06:33:27
oeisdata/seq/A363/A363700.seq
51b12fb5bebb81405c84466d09e56df0