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christopher
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oeis

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int64
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2.35k
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-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A356101
Intersection of A000201 and A022839.
[ "1", "3", "9", "12", "14", "16", "19", "21", "25", "27", "30", "32", "37", "43", "45", "48", "50", "56", "59", "61", "63", "66", "72", "74", "77", "79", "85", "88", "90", "92", "95", "97", "101", "103", "106", "108", "110", "113", "119", "121", "124", "126", "132", "135", "137", "139", "142", "144", "148", "150", "153", "155", "161", "166", "168", "171", "173", "177", "179" ]
[ "nonn", "easy" ]
22
1
2
[ "A000201", "A001950", "A022839", "A108598", "A190509", "A351415", "A356101", "A356102", "A356103", "A356104" ]
null
Clark Kimberling, Sep 04 2022
2023-06-05T08:56:17
oeisdata/seq/A356/A356101.seq
f0e64ad49fd73ed2c8de1a48b212747f
A356102
Intersection of A001950 and A022839.
[ "2", "13", "15", "20", "26", "31", "44", "49", "60", "62", "73", "78", "89", "91", "96", "102", "107", "109", "120", "125", "136", "138", "143", "149", "154", "167", "172", "178", "183", "185", "196", "201", "212", "214", "219", "225", "230", "243", "248", "259", "261", "272", "277", "290", "295", "301", "306", "308", "319", "324", "326", "328", "330", "333", "335" ]
[ "nonn", "easy" ]
15
1
1
[ "A000201", "A001950", "A022839", "A108598", "A190509", "A351415", "A356101", "A356102", "A356103", "A356104" ]
null
Clark Kimberling, Sep 04 2022
2022-11-19T20:35:15
oeisdata/seq/A356/A356102.seq
230dc1866d700e313552c7fd55571b4b
A356103
Intersection of A001950 and A108598.
[ "5", "7", "10", "18", "23", "28", "34", "36", "39", "41", "47", "52", "54", "57", "65", "68", "70", "75", "81", "83", "86", "94", "99", "104", "112", "115", "117", "123", "128", "130", "133", "141", "146", "151", "157", "159", "162", "164", "170", "175", "180", "188", "191", "193", "198", "204", "206", "209", "217", "222", "227", "233", "235", "238", "240", "246", "251" ]
[ "nonn", "easy" ]
15
1
1
[ "A000201", "A001950", "A022839", "A108598", "A190509", "A351415", "A356101", "A356102", "A356103", "A356104" ]
null
Clark Kimberling, Sep 04 2022
2022-11-19T20:35:26
oeisdata/seq/A356/A356103.seq
ae163409b8de699695a9e309fd219730
A356104
a(n) = A000201(A022839(n)).
[ "3", "6", "9", "12", "17", "21", "24", "27", "32", "35", "38", "42", "46", "50", "53", "56", "61", "64", "67", "71", "74", "79", "82", "85", "88", "93", "97", "100", "103", "108", "111", "114", "118", "122", "126", "129", "132", "135", "140", "144", "147", "150", "155", "158", "161", "165", "169", "173", "176", "179", "184", "187", "190", "194", "197", "202", "205", "208" ]
[ "nonn", "easy" ]
14
1
1
[ "A000201", "A001950", "A022839", "A108598", "A351415", "A356104", "A356105", "A356106", "A356107", "A356217" ]
null
Clark Kimberling, Sep 08 2022
2025-03-23T04:34:49
oeisdata/seq/A356/A356104.seq
067c33452e11c63400ac0af9f31e27b0
A356105
a(n) = A000201(A108598(n)).
[ "1", "4", "8", "11", "14", "16", "19", "22", "25", "29", "30", "33", "37", "40", "43", "45", "48", "51", "55", "58", "59", "63", "66", "69", "72", "76", "77", "80", "84", "87", "90", "92", "95", "98", "101", "105", "106", "110", "113", "116", "119", "121", "124", "127", "131", "134", "137", "139", "142", "145", "148", "152", "153", "156", "160", "163", "166", "168", "171" ]
[ "nonn", "easy" ]
10
1
2
[ "A000201", "A001950", "A022839", "A108598", "A351415", "A356104", "A356105", "A356106", "A356107", "A356217" ]
null
Clark Kimberling, Sep 08 2022
2025-03-23T04:34:45
oeisdata/seq/A356/A356105.seq
6b2821afea05712822a008bbe63f5d61
A356106
a(n) = A001950(A022839(n)).
[ "5", "10", "15", "20", "28", "34", "39", "44", "52", "57", "62", "68", "75", "81", "86", "91", "99", "104", "109", "115", "120", "128", "133", "138", "143", "151", "157", "162", "167", "175", "180", "185", "191", "198", "204", "209", "214", "219", "227", "233", "238", "243", "251", "256", "261", "267", "274", "280", "285", "290", "298", "303", "308", "314", "319" ]
[ "nonn", "easy" ]
18
1
1
[ "A000201", "A001950", "A022839", "A108598", "A351415", "A356104", "A356105", "A356106", "A356107", "A356217" ]
null
Clark Kimberling, Sep 08 2022
2025-03-23T04:34:34
oeisdata/seq/A356/A356106.seq
c643e34daaaae655773c966e419fd0ef
A356107
a(n) = A001950(A108598(n)).
[ "2", "7", "13", "18", "23", "26", "31", "36", "41", "47", "49", "54", "60", "65", "70", "73", "78", "83", "89", "94", "96", "102", "107", "112", "117", "123", "125", "130", "136", "141", "146", "149", "154", "159", "164", "170", "172", "178", "183", "188", "193", "196", "201", "206", "212", "217", "222", "225", "230", "235", "240", "246", "248", "253", "259", "264" ]
[ "nonn", "easy" ]
11
1
1
[ "A000201", "A001950", "A022839", "A108598", "A351415", "A356104", "A356105", "A356106", "A356107", "A356217" ]
null
Clark Kimberling, Oct 02 2022
2025-03-23T04:34:31
oeisdata/seq/A356/A356107.seq
0284377cd2f82a05b41a970db9f7ce99
A356108
Numbers == 2 (mod 6) that cannot be written as p^2 + q where p and q are primes.
[ "2", "8", "74", "170", "614", "704", "1010", "24476" ]
[ "nonn", "more" ]
6
1
1
[ "A356077", "A356108" ]
null
J. M. Bergot and Robert Israel, Jul 27 2022
2022-08-23T10:18:16
oeisdata/seq/A356/A356108.seq
e25b0e97aaad7a32ee61bd49b5158267
A356109
Numbers k such that k^2 + {1,3,7,13} are prime.
[ "2", "4", "10", "5996", "8894", "11204", "14290", "23110", "30866", "37594", "43054", "64390", "74554", "83464", "93460", "109456", "111940", "132304", "151904", "184706", "238850", "262630", "265990", "277630", "300206", "315410", "352600", "355450", "376190", "404954", "415180", "462830", "483494", "512354", "512704", "566296" ]
[ "nonn" ]
17
1
1
[ "A005574", "A049422", "A113536", "A114270", "A182238", "A356109" ]
null
Michel Lagneau, Jul 27 2022
2022-07-28T03:51:24
oeisdata/seq/A356/A356109.seq
9fc46249293912fd8737e41c1fcf22f7
A356110
Numbers k such that k^2 + {1,3,7,13,31} are prime.
[ "4", "10", "14290", "43054", "109456", "315410", "352600", "483494", "566296", "685114", "927070", "1106116", "1248796", "1501174", "1997986", "2399204", "2501404", "2553100", "2726840", "2874680", "3291760", "4129394", "4473766", "4794520", "4901144", "6350306", "7444070", "7753456", "7892504", "8009536", "8069540" ]
[ "nonn" ]
15
1
1
[ "A005574", "A049422", "A113536", "A114270", "A182238", "A356109", "A356110" ]
null
Michel Lagneau, Jul 27 2022
2022-07-28T03:52:10
oeisdata/seq/A356/A356110.seq
6b461e7089540fb397b54551d8fb6fba
A356111
The number of 1+1+1-free ordered posets of [n].
[ "1", "1", "2", "6", "23", "102", "497", "2586", "14127", "80146", "468688", "2810163", "17206549", "107261051", "679096359", "4358360362", "28309516828", "185862601727", "1232042778231", "8238155634738", "55521191613041", "376888928783870", "2575334987109807", "17704834935517727", "122401523831513816" ]
[ "nonn" ]
19
0
3
[ "A001181", "A006455", "A135922", "A356111" ]
null
David Bevan, Jul 27 2022
2024-10-05T09:41:02
oeisdata/seq/A356/A356111.seq
cc9835e74e3ed96f43cec7d9bf5ebd84
A356112
Direction of segment n in the E curve of Dekking and McKenna.
[ "1", "1", "2", "-1", "2", "1", "2", "-1", "-1", "2", "1", "1", "1", "2", "1", "-2", "-2", "-1", "-2", "-2", "1", "2", "1", "-2", "-2", "1", "1", "2", "-1", "2", "1", "2", "-1", "-1", "2", "1", "1", "1", "2", "1", "-2", "-2", "-1", "-2", "-2", "1", "2", "1", "-2", "-2", "1", "1", "2", "-1", "2", "1", "1", "-2", "1", "1", "2", "-1", "2", "2", "2", "-1", "-2", "-2", "-1", "2", "-1", "-2", "-1", "2", "2", "2", "2", "-1", "-2", "-1", "2", "2", "1", "2", "2", "-1", "-2", "-1", "-1", "-1", "-2", "1", "1", "-2", "-1", "-2", "1", "-2", "-1", "-1", "2", "2", "-1", "-2" ]
[ "sign" ]
42
0
3
[ "A229214", "A261180", "A356112" ]
null
Arie Bos, Jul 27 2022
2022-07-30T19:39:40
oeisdata/seq/A356/A356112.seq
17dc4172a138a04a8b6c4fff54082890
A356113
Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.
[ "1", "1", "1", "1", "1", "5", "1", "1", "10", "6", "16", "1", "1", "17", "25", "54", "58", "42", "1", "1", "26", "46", "27", "137", "354", "63", "224", "330", "99", "1", "1", "37", "77", "105", "291", "906", "513", "567", "817", "2883", "957", "811", "1466", "219", "1", "1", "50", "120", "188", "108", "548", "2020", "2632", "1508", "1682", "2356", "10116", "5574", "11724", "978", "4184", "18128", "8436", "2722", "5668", "466", "1" ]
[ "nonn", "tabf" ]
12
0
6
[ "A174159", "A355776", "A355777", "A356113", "A356118" ]
null
Peter Luschny, Jul 28 2022
2022-08-23T05:21:37
oeisdata/seq/A356/A356113.seq
1f6e85dcdfe1980d0ed8e14f09edd17b
A356114
Number of irreducible permutations of n with partition type [2, 1, 1, ..., 1] (with '1' taken n - 2 times).
[ "0", "0", "0", "2", "9", "24", "55", "118", "245", "500", "1011", "2034", "4081", "8176", "16367", "32750", "65517", "131052", "262123", "524266", "1048553", "2097128", "4194279", "8388582", "16777189", "33554404", "67108835", "134217698", "268435425", "536870880", "1073741791", "2147483614", "4294967261", "8589934556", "17179869147" ]
[ "nonn", "easy" ]
19
0
4
[ "A079500", "A355777", "A356114", "A356262", "A356263" ]
null
Peter Luschny, Aug 01 2022
2022-08-18T09:18:17
oeisdata/seq/A356/A356114.seq
9226c0c4a1f29931d57cf93feca0e0a1
A356115
Triangle read by rows. The reduced triangle of the partition triangle of reducible permutations with weakly decreasing Lehmer code (A356266). T(n, k) for n >= 1 and 0 <= k < n.
[ "1", "0", "1", "0", "1", "1", "0", "3", "1", "1", "0", "4", "6", "3", "1", "0", "9", "20", "6", "6", "1", "0", "11", "45", "50", "15", "10", "1", "0", "19", "93", "185", "80", "36", "15", "1", "0", "22", "196", "462", "490", "161", "77", "21", "1", "0", "33", "312", "1120", "1834", "1050", "336", "148", "28", "1" ]
[ "nonn", "tabl" ]
8
1
8
[ "A120588", "A356115", "A356265", "A356266" ]
null
Peter Luschny, Aug 16 2022
2022-08-21T14:09:48
oeisdata/seq/A356/A356115.seq
0e4359a7965d6c716135473d5d282291
A356116
Triangle read by row. The reduced triangle of the partition_triangle A355776.
[ "0", "0", "0", "0", "1", "0", "0", "5", "5", "0", "0", "16", "46", "16", "0", "0", "42", "252", "252", "42", "0", "0", "99", "1086", "2241", "1086", "99", "0", "0", "219", "4097", "15129", "15129", "4097", "219", "0", "0", "466", "14272", "87058", "154426", "87058", "14272", "466", "0", "0", "968", "47300", "452672", "1305062", "1305062", "452672", "47300", "968", "0" ]
[ "nonn", "tabl" ]
13
1
8
[ "A002662", "A056986", "A355776", "A356116" ]
null
Peter Luschny, Jul 28 2022
2022-08-23T05:47:09
oeisdata/seq/A356/A356116.seq
01a06ee492535f4dc5639432c2c89813
A356117
T(n, k) = [x^k] (1/2 - x)^(-n) - (1 - x)^(-n).
[ "0", "1", "3", "3", "14", "45", "7", "45", "186", "630", "15", "124", "630", "2540", "8925", "31", "315", "1905", "8925", "35770", "128898", "63", "762", "5355", "28616", "128898", "515844", "1891890", "127", "1785", "14308", "85932", "429870", "1891890", "7568484", "28113228", "255", "4088", "36828", "245640", "1351350", "6487272", "28113228", "112456344", "421717725" ]
[ "nonn", "tabl" ]
14
0
3
[ "A000225", "A059672", "A059937", "A131568", "A134346", "A327318", "A356117" ]
null
Peter Luschny, Aug 22 2022
2022-08-23T13:37:33
oeisdata/seq/A356/A356117.seq
6601fed3667ad500a4fe2be1e0952f4f
A356118
Row sums of A174159.
[ "1", "1", "2", "7", "34", "198", "1308", "9651", "79210", "720898", "7240804", "79774814", "957795188", "12453298700", "174353907960", "2615339041155", "41845544418330", "711374726547210", "12804746933817300", "243290199050400810", "4865804009789159580", "102181884318952612980", "2248001455463732796360" ]
[ "nonn" ]
4
0
3
[ "A174159", "A356118" ]
null
Peter Luschny, Jul 27 2022
2022-07-27T16:35:48
oeisdata/seq/A356/A356118.seq
caf5a25314b3750f7c167323ef61742a
A356119
Irregular table read by rows: T(n,k) is the number of k-sided polygons formed, for k>=3, in an equilateral triangle when straight line segments connect the three corner vertices to the points dividing the sides into n equal parts.
[ "1", "6", "12", "3", "3", "1", "24", "6", "36", "9", "9", "7", "48", "24", "6", "72", "21", "15", "19", "84", "48", "12", "6", "108", "51", "33", "25", "132", "78", "18", "18", "168", "69", "51", "43", "180", "120", "48", "18", "216", "135", "57", "61", "252", "156", "66", "36", "294", "159", "105", "67", "312", "234", "84", "48", "372", "225", "117", "103", "408", "264", "138", "60", "456", "291", "159", "121", "486", "372", "138", "84" ]
[ "nonn", "tabf" ]
17
1
2
[ "A092098", "A331782", "A332376", "A335413", "A356119" ]
null
Scott R. Shannon, Jul 27 2022
2022-07-27T10:33:01
oeisdata/seq/A356/A356119.seq
6993581d600cdb4a1d26c5d528be4621
A356120
Irregular triangle read by rows: the n-th row lists the values 0..2^n-1 representing all subsets of a set of n elements. When its elements are linearly ordered, the subsets are lexicographically ordered.
[ "0", "0", "1", "0", "2", "3", "1", "0", "4", "6", "7", "5", "2", "3", "1", "0", "8", "12", "14", "15", "13", "10", "11", "9", "4", "6", "7", "5", "2", "3", "1", "0", "16", "24", "28", "30", "31", "29", "26", "27", "25", "20", "22", "23", "21", "18", "19", "17", "8", "12", "14", "15", "13", "10", "11", "9", "4", "6", "7", "5", "2", "3", "1", "0", "32", "48", "56", "60", "62", "63", "61", "58", "59", "57", "52", "54", "55", "53", "50", "51", "49", "40", "44", "46", "47", "45", "42" ]
[ "nonn", "tabf" ]
30
0
5
[ "A000004", "A000225", "A006516", "A007283", "A108918", "A110286", "A131577", "A135092", "A356120" ]
null
Valentin Bakoev, Jul 27 2022
2023-01-08T16:29:42
oeisdata/seq/A356/A356120.seq
9c9c858659ba700bff7f15373bcde698
A356121
Matula-Goebel number of the rooted binary tree with Colijn-Plazzotta number n.
[ "1", "4", "14", "49", "86", "301", "1849", "454", "1589", "9761", "51529", "886", "3101", "19049", "100561", "196249", "3986", "13951", "85699", "452411", "882899", "3972049", "31754", "111139", "682711", "3604079", "7033511", "31642861", "252079129", "6418", "22463", "137987", "728443", "1421587", "6395537", "50949293", "10297681" ]
[ "nonn" ]
18
1
2
[ "A002024", "A002260", "A111299", "A356121" ]
null
Kevin Ryde, Jul 31 2022
2024-12-19T11:46:19
oeisdata/seq/A356/A356121.seq
68c60eb66588fd1a409f5ab40845f0aa
A356122
Number of Lucas divisors of the n-th Lucas number.
[ "2", "1", "2", "3", "2", "2", "4", "2", "2", "4", "3", "2", "4", "2", "3", "5", "2", "2", "5", "2", "3", "5", "3", "2", "4", "3", "3", "5", "3", "2", "6", "2", "2", "5", "3", "4", "5", "2", "3", "5", "3", "2", "6", "2", "3", "7", "3", "2", "4", "3", "4", "5", "3", "2", "6", "4", "3", "5", "3", "2", "6", "2", "3", "7", "2", "4", "6", "2", "3", "5", "5", "2", "5", "2", "3", "7", "3", "4", "6", "2", "3", "6", "3", "2", "6", "4", "3", "5", "3", "2", "8", "4", "3", "5", "3", "4", "4", "2", "4", "7" ]
[ "nonn" ]
14
0
1
[ "A000032", "A076984", "A102460", "A304092", "A356062", "A356122", "A356123" ]
null
Michel Marcus, Jul 27 2022
2022-08-25T16:22:40
oeisdata/seq/A356/A356122.seq
ec70b8572331ebc31d2961104565baf3
A356123
Least Lucas number with n Lucas divisors.
[ "1", "2", "4", "18", "1364", "1860498", "2537720636", "6440026026380244498", "8784200221406821330636", "77162173529763648886126034136172445632164498", "4365101043708483494615466932242949707161871659736799144058331102381689400753867700636" ]
[ "nonn" ]
18
1
2
[ "A000032", "A076985", "A102460", "A304092", "A356062", "A356122", "A356123", "A356666" ]
null
Michel Marcus, Jul 27 2022
2022-08-24T12:09:06
oeisdata/seq/A356/A356123.seq
39a7cbdeee8e4ac0a3923c26fe6f3c36
A356124
Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} j^k * binomial(floor(n/j)+1,2).
[ "1", "1", "4", "1", "5", "8", "1", "7", "11", "15", "1", "11", "19", "23", "21", "1", "19", "41", "47", "33", "33", "1", "35", "103", "125", "77", "57", "41", "1", "67", "281", "395", "255", "149", "71", "56", "1", "131", "799", "1373", "1025", "555", "205", "103", "69", "1", "259", "2321", "5027", "4503", "2537", "905", "325", "130", "87", "1", "515", "6823", "18965", "20657", "12867", "4945", "1585", "442", "170", "99" ]
[ "nonn", "tabl" ]
32
1
3
[ "A024916", "A143127", "A143128", "A279394", "A319649", "A350106", "A356124", "A356125", "A356126", "A356128", "A356129" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-24T12:40:11
oeisdata/seq/A356/A356124.seq
c6dd8c443dde5c71690c48e6c816680a
A356125
a(n) = Sum_{k=1..n} k * sigma_2(k).
[ "1", "11", "41", "125", "255", "555", "905", "1585", "2404", "3704", "5046", "7566", "9776", "13276", "17176", "22632", "27562", "35752", "42630", "53550", "64050", "77470", "89660", "110060", "126335", "148435", "170575", "199975", "224393", "263393", "293215", "336895", "377155", "426455", "471955", "540751", "591441", "660221", "726521" ]
[ "nonn" ]
26
1
2
[ "A319086", "A328259", "A356042", "A356124", "A356125" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-22T00:47:56
oeisdata/seq/A356/A356125.seq
f2a4066d9f7f2416189b9ee587f09ea7
A356126
a(n) = Sum_{k=1..n} k * sigma_3(k).
[ "1", "19", "103", "395", "1025", "2537", "4945", "9625", "16438", "27778", "42430", "66958", "95532", "138876", "191796", "266692", "350230", "472864", "603204", "787164", "989436", "1253172", "1533036", "1926156", "2319931", "2834263", "3386143", "4089279", "4796589", "5749149", "6672701", "7871069", "9101837", "10605521" ]
[ "nonn" ]
20
1
2
[ "A281372", "A356043", "A356124", "A356126" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-24T15:42:28
oeisdata/seq/A356/A356126.seq
d73912190cd3f5e8b5086128468fa7e0
A356127
a(n) = Sum_{k=1..n} k^k * binomial(floor(n/k)+1,2).
[ "1", "7", "37", "305", "3435", "50163", "873713", "17651465", "405072044", "10405078324", "295716748946", "9211817291426", "312086923883692", "11424093751088836", "449317984131957736", "18896062057875064856", "846136323944211829050", "40192544399241524385636" ]
[ "nonn" ]
17
1
2
[ "A355887", "A355950", "A356127" ]
null
Seiichi Manyama, Jul 27 2022
2022-07-28T15:20:42
oeisdata/seq/A356/A356127.seq
3f61acc129d2d83e09e76d23a24e03ef
A356128
a(n) = Sum_{k=1..n} k * sigma_n(k).
[ "1", "11", "103", "1373", "20657", "381795", "7921825", "187452793", "4916743582", "142471278944", "4506381463150", "154747691135574", "5729252807696052", "227595085199164036", "9654855890695727316", "435664037303036699736", "20836069678062430493950", "1052867409176853099312712" ]
[ "nonn" ]
21
1
2
[ "A356046", "A356124", "A356128" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-24T15:43:33
oeisdata/seq/A356/A356128.seq
cc6cdf646adef425ffde023c4826122a
A356129
a(n) = Sum_{k=1..n} k * sigma_{n-1}(k).
[ "1", "7", "41", "395", "4503", "68969", "1205345", "24831145", "574932340", "14936279962", "427782949566", "13426887958078", "457622797727840", "16842616079514468", "665489067204502336", "28102162931539093732", "1262904299189373463930", "60182778247311758955112" ]
[ "nonn" ]
22
1
2
[ "A356124", "A356129", "A356130", "A356131" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-24T15:43:37
oeisdata/seq/A356/A356129.seq
96dfebb73cb06967d4b863ab937ff870
A356130
a(n) = Sum_{k=1..n} sigma_{n-1}(k).
[ "1", "4", "16", "111", "999", "12513", "185683", "3316418", "67810767", "1576561677", "40862702931", "1171104916405", "36722498575799", "1251419967587955", "46034784688102781", "1818440444592581068", "76763036794222996512", "3448830049286378614987", "164309958491233496689189" ]
[ "nonn" ]
20
1
2
[ "A319194", "A319649", "A356129", "A356130" ]
null
Seiichi Manyama, Jul 27 2022
2023-10-21T19:39:06
oeisdata/seq/A356/A356130.seq
40ab9bd6a368b81784df5622cb2314dc
A356131
a(n) = Sum_{k=1..n} (k - 1)^n * binomial(floor(n/k)+1,2).
[ "0", "1", "9", "100", "1302", "20648", "377022", "7921039", "186926431", "4916562309", "142373072781", "4506381442625", "154721361953489", "5729251983077521", "227585590018322461", "9654855432715969784", "435659531345223039702", "20836069677785611552293" ]
[ "nonn" ]
16
1
3
[ "A350109", "A356100", "A356129", "A356131" ]
null
Seiichi Manyama, Jul 27 2022
2022-07-28T15:50:35
oeisdata/seq/A356/A356131.seq
8280af3e7ebe78f8022f057bf6305f1f
A356132
Least integer with n pentagonal divisors.
[ "1", "5", "35", "70", "210", "420", "2310", "4620", "18480", "32340", "60060", "120120", "240240", "720720", "1261260", "1141140", "2042040", "4084080", "4564560", "13693680", "19399380", "58198140", "95855760", "38798760", "116396280", "193993800", "77597520", "232792560", "543182640", "387987600", "1125164040" ]
[ "nonn" ]
9
1
2
[ "A000326", "A130317", "A279497", "A356132" ]
null
Michel Marcus, Jul 27 2022
2022-07-27T16:35:18
oeisdata/seq/A356/A356132.seq
8093e2c9932e062c530fade93ea6350e
A356133
Complement of A026430.
[ "2", "4", "7", "11", "13", "17", "20", "22", "25", "29", "32", "34", "38", "40", "43", "47", "49", "53", "56", "58", "62", "64", "67", "71", "74", "76", "79", "83", "85", "89", "92", "94", "97", "101", "104", "106", "110", "112", "115", "119", "122", "124", "127", "131", "133", "137", "140", "142", "146", "148", "151", "155", "157", "161", "164", "166", "169", "173", "176" ]
[ "nonn", "easy" ]
26
1
1
[ "A001285", "A007413", "A026430", "A036554", "A036580", "A091855", "A354384", "A356133" ]
null
Clark Kimberling, Aug 04 2022
2023-03-01T14:28:26
oeisdata/seq/A356/A356133.seq
882683db6dddf11a585a1ad8472bb6ba
A356134
Triangular array giving total number of legal Go positions on an n X k board.
[ "1", "5", "57", "15", "489", "12675", "41", "4125", "321689", "24318165", "113", "35117", "8180343", "1840058693", "414295148741", "313", "299681", "208144601", "139304759213", "93332304864173", "62567386502084877", "867", "2557605", "5296282323", "10546705714473", "21026744638200555", "41945191530093646965", "83677847847984287628595" ]
[ "nonn", "tabl" ]
30
1
2
[ "A094777", "A102620", "A266278", "A356049", "A356134" ]
null
Douglas Boffey, Jul 27 2022
2025-06-27T21:32:51
oeisdata/seq/A356/A356134.seq
b65a3ec4af7067284ef35d1a7e4e5bae
A356135
Semiprimes k such that k is congruent to 6 modulo k's index in the sequence of semiprimes.
[ "4", "6", "9", "10", "22", "26", "177", "183", "213", "27662", "3066886", "3067021", "3067161", "3067166", "3067186", "3067241", "3067271", "3067421", "3067426", "3067541", "3067561", "3067571", "3067586", "3067661", "3067681", "3067711", "3067741", "3067901", "3067906", "3067991", "3068041", "44690978177", "44690978534", "44690978639", "44690978891" ]
[ "nonn", "hard" ]
14
1
1
[ "A001358", "A106131", "A356135" ]
null
Lucas A. Brown, Oct 14 2022
2023-01-24T16:45:06
oeisdata/seq/A356/A356135.seq
f1c8388622e2887b4477bddeb07d8edc
A356136
a(n) is the smallest number k > 1 such that, in the interval 1..k, there are as many integers that have exactly 2n divisors as there are primes (or -1 if no such number exists).
[ "2", "27", "-1", "665", "-1", "57675", "-1", "57230", "-1" ]
[ "sign", "hard", "more" ]
22
1
1
[ "A000010", "A356136" ]
null
Jon E. Schoenfield, Oct 14 2022
2022-10-18T13:26:57
oeisdata/seq/A356/A356136.seq
5be2c25225e093bdae87656294b683ea
A356137
Positive integers m such that the fractional part of the geometric mean of the sequence s(m) does not exceed the fractional part of the arithmetic mean of s(m), where s(m) is the sequence 1 + 1/1, 2 + 1/2, ..., m + 1/m.
[ "1", "2", "3", "5", "6", "8", "10", "13", "14", "16", "18", "22", "24", "26", "30", "32", "34", "38", "40", "42", "46", "48", "54", "56", "61", "62", "64", "69", "70", "72", "78", "80", "86", "88", "92", "94", "96", "100", "102", "108", "110", "115", "116", "118", "124", "126", "132", "134", "138", "140", "146", "148", "154", "156", "161", "162", "164", "170", "172", "178", "180" ]
[ "nonn" ]
60
1
2
[ "A102928", "A356137", "A356142" ]
null
Mike Jones, Jul 27 2022
2022-07-31T23:11:03
oeisdata/seq/A356/A356137.seq
b986b17c8cbba33692af50bc01565e81
A356138
a(n) = A137803(A001951(n)).
[ "1", "3", "7", "9", "13", "15", "17", "21", "22", "26", "28", "30", "34", "36", "40", "42", "45", "47", "49", "53", "55", "59", "61", "63", "66", "68", "72", "74", "78", "80", "82", "86", "88", "91", "93", "95", "99", "101", "105", "107", "109", "112", "114", "118", "120", "124", "126", "128", "132", "133", "137", "139", "141", "145", "147", "151", "153", "156", "158", "160" ]
[ "nonn", "easy" ]
16
1
2
[ "A001951", "A001952", "A137804", "A356056", "A356057", "A356058", "A356059", "A356138", "A356139", "A356140", "A356141" ]
null
Clark Kimberling, Aug 06 2022
2025-03-23T18:38:28
oeisdata/seq/A356/A356138.seq
3247c8886546afefe4dc609426652a1a
A356139
a(n) = A137804(A001951(n)).
[ "2", "4", "8", "10", "14", "16", "18", "23", "25", "29", "31", "33", "37", "39", "43", "46", "50", "52", "54", "58", "60", "64", "67", "69", "73", "75", "79", "81", "85", "87", "90", "94", "96", "100", "102", "104", "108", "110", "115", "117", "119", "123", "125", "129", "131", "136", "138", "140", "144", "146", "150", "152", "154", "159", "161", "165", "167", "171", "173" ]
[ "nonn", "easy" ]
14
1
1
[ "A001951", "A001952", "A137804", "A356056", "A356057", "A356058", "A356059", "A356138", "A356139", "A356140", "A356141" ]
null
Clark Kimberling, Aug 06 2022
2025-03-23T04:34:27
oeisdata/seq/A356/A356139.seq
02818d3b0a311b47fc355e0ec4a8f208
A356140
a(n) = A137803(A001952(n)).
[ "5", "11", "19", "24", "32", "38", "44", "51", "57", "65", "70", "76", "84", "89", "97", "103", "111", "116", "122", "130", "135", "143", "149", "155", "162", "168", "176", "181", "189", "195", "200", "208", "214", "222", "227", "233", "241", "246", "254", "260", "266", "273", "279", "287", "292", "300", "306", "312", "319", "325", "333", "338", "344", "352", "357" ]
[ "nonn", "easy" ]
14
1
1
[ "A001951", "A001952", "A137804", "A356056", "A356057", "A356058", "A356059", "A356138", "A356139", "A356140", "A356141" ]
null
Clark Kimberling, Aug 06 2022
2025-03-23T04:34:24
oeisdata/seq/A356/A356140.seq
dee1b9a5e0a5ae13dc52344e8601558b
A356141
a(n) = A137804(A001952(n)).
[ "6", "12", "20", "27", "35", "41", "48", "56", "62", "71", "77", "83", "92", "98", "106", "113", "121", "127", "134", "142", "148", "157", "163", "169", "177", "184", "192", "198", "207", "213", "219", "228", "234", "242", "249", "255", "263", "270", "278", "284", "291", "299", "305", "314", "320", "328", "335", "341", "349", "355", "364", "370", "376", "385", "391" ]
[ "nonn", "easy" ]
13
1
1
[ "A001951", "A001952", "A137804", "A356056", "A356057", "A356058", "A356059", "A356138", "A356139", "A356140", "A356141" ]
null
Clark Kimberling, Aug 06 2022
2025-03-23T04:34:21
oeisdata/seq/A356/A356141.seq
d353a7d1f2f09bd5512b9d4b0f166348
A356142
a(n) is the reduced numerator of the arithmetic mean of the first n terms of the sequence [n + 1/n, n > 0].
[ "2", "9", "47", "145", "1037", "469", "4283", "10841", "120529", "145981", "1913231", "2248181", "33938753", "39009533", "44438957", "100454479", "1916734943", "712651981", "15018824599", "662986195", "1213859861", "1327904701", "33283587163", "108432400555", "2934259832467", "3166619637067", "30671014001603", "32922658468103" ]
[ "nonn", "frac" ]
7
1
1
[ "A102928", "A356137", "A356142" ]
null
Stefano Spezia, Jul 27 2022
2022-07-29T09:53:58
oeisdata/seq/A356/A356142.seq
17cb72b7d5903f32a9e0d7e796693eaf
A356143
Numbers that can be written in two or more ways as the product of three divisors greater than 1 such that the number in binary is contained in the string concatenation of the divisors in binary.
[ "126", "252", "495", "504", "1008", "2016", "3420", "3510", "4032", "5850", "8064", "11700", "16128", "23400", "32256", "46800", "64512", "93600", "129024", "187200", "258048", "374400", "516096", "748800", "1032192", "1497600", "2064384", "2995200", "4128768", "5990400", "8257536", "11980800", "16515072", "23961600", "33030144", "47923200", "57587274", "66060288" ]
[ "nonn", "base" ]
26
1
1
[ "A027750", "A030190", "A210959", "A355790", "A355791", "A355852", "A355857", "A356143", "A356176" ]
null
Scott R. Shannon, Jul 30 2022
2022-07-30T14:14:47
oeisdata/seq/A356/A356143.seq
9b78acc0ca1d9dc04e6a519b80231a4b
A356144
Coefficients of the set of partition polynomials [RT] = [P][E]; i.e., coefficients of polynomials resulting from using the set of refined Eulerian polynomials, [E], of A145271 as the indeterminates of the set of permutahedra polynomials, [P], of A133314. Irregular triangle read by rows with lengths given by A000041.
[ "1", "-1", "1", "-1", "-1", "2", "-1", "1", "-3", "2", "1", "-1", "-1", "4", "-4", "-2", "5", "-1", "-1", "1", "-5", "8", "2", "-4", "-2", "-4", "5", "4", "-4", "-1", "-1", "6", "-12", "-3", "8", "18", "-6", "-14", "13", "2", "-16", "14", "0", "-8", "-1", "1", "-7", "18", "3", "-20", "0", "-15", "8", "18", "57", "6", "-54", "-15", "-12", "84", "-30", "-48", "14", "14", "-8", "-13", "-1", "-1", "8", "-24", "-4", "32", "51", "-27", "-16", "-6", "171", "-42", "-177", "50", "90", "-18", "456", "-276", "-246", "-15", "30", "154", "-42", "124", "-166", "-113", "42", "6", "-21", "-19", "-1" ]
[ "sign", "tabf" ]
46
0
6
[ "A000108", "A133314", "A133437", "A134685", "A145271", "A263633", "A355201", "A356144", "A356145" ]
null
Tom Copeland, Jul 27 2022
2024-02-17T12:32:29
oeisdata/seq/A356/A356144.seq
2db3f00f2ea55ac6af8c7dabd0886ce0
A356145
Coefficients of the inverse refined Eulerian partition polynomials [E]^{-1}, partitional inverse to A145271. Irregular triangle read by row with lengths A000041.
[ "1", "1", "-1", "1", "3", "-4", "1", "-15", "25", "-4", "-7", "1", "105", "-210", "70", "60", "-15", "-11", "1", "-945", "2205", "-1120", "-630", "70", "350", "126", "-15", "-26", "-16", "1", "10395", "-27720", "18900", "7875", "-2800", "-6930", "-1638", "560", "455", "784", "238", "-56", "-42", "-22", "1", "-135135", "405405", "-346500", "-114345", "84700" ]
[ "sign", "tabf" ]
46
0
5
[ "A000041", "A006351", "A112493", "A124324", "A133314", "A134685", "A134991", "A145271", "A356144", "A356145" ]
null
Tom Copeland, Jul 27 2022
2025-03-29T22:09:19
oeisdata/seq/A356/A356145.seq
3910f5f6ff5744ee52241755ffab81bd
A356146
Coefficients of the partition polynomials that are binomial convolutions of the partition polynomials of A133314, the refined Euler characteristic polynomials of the permutahedra and coefficient polynomials of reciprocals of Taylor series or e.g.f.s. Irregular triangle read by rows with length given by A000041.
[ "1", "1", "-3", "1", "12", "-9", "1", "-60", "72", "-9", "-12", "1", "360", "-600", "180", "120", "-30", "-15", "1", "-2520", "5400", "-2700", "-1200", "180", "720", "180", "-30", "-45", "-18", "1", "20160", "-52920", "37800", "12600", "-6300", "-12600", "-2100", "1260", "840", "1260", "252", "-105", "-63", "-21", "1" ]
[ "sign", "tabf" ]
21
0
3
[ "A000041", "A133314", "A356146" ]
null
Tom Copeland, Jul 27 2022
2024-03-28T23:53:28
oeisdata/seq/A356/A356146.seq
45676fe6e3e1e29e67cbfef5a15c0aab
A356147
Lower twin primes whose sum of digits is a lower twin prime.
[ "3", "5", "29", "41", "137", "179", "191", "197", "227", "269", "281", "311", "461", "641", "809", "821", "827", "881", "1019", "1031", "1091", "1277", "1301", "1451", "1619", "1721", "1871", "2027", "2081", "2087", "2111", "2267", "2339", "2591", "2711", "2801", "2999", "3167", "3251", "3257", "3329", "3527", "3581", "3671", "3851", "4001", "4049", "4157", "4229", "4241", "4337", "4421", "4481" ]
[ "nonn", "base" ]
13
1
1
[ "A001359", "A007953", "A046704", "A356147" ]
null
J. M. Bergot and Robert Israel, Jul 27 2022
2022-08-23T18:16:30
oeisdata/seq/A356/A356147.seq
5a76d75826f884f20d77f98a0d1830db
A356148
a(n) is the number of positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.
[ "1", "2", "2", "4", "3", "4", "3", "6", "6", "4", "6", "6", "6", "6", "4", "8", "9", "9", "8", "8", "5", "9", "9", "9", "8", "8", "9", "9", "9", "8", "5", "10", "12", "13", "12", "12", "12", "10", "12", "12", "12", "6", "10", "12", "12", "13", "12", "12", "12", "12", "10", "12", "10", "12", "13", "12", "12", "12", "13", "12", "12", "10", "6", "12", "15", "17", "16", "17", "17", "16", "15", "17", "15" ]
[ "nonn", "base" ]
12
1
2
[ "A004277", "A122953", "A356148", "A356149", "A356150" ]
null
Rémy Sigrist, Jul 28 2022
2022-07-31T19:53:44
oeisdata/seq/A356/A356148.seq
22c29c7f9d8e2f5e54ec5ba304aef2d4
A356149
Irregular table T(n, k), n > 0, k = 1..A356148(n), read by rows; the n-th row contains, in ascending order, the distinct positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.
[ "1", "1", "2", "1", "3", "1", "2", "3", "4", "1", "2", "5", "1", "2", "3", "6", "1", "3", "7", "1", "2", "3", "4", "7", "8", "1", "2", "3", "4", "6", "9", "1", "2", "5", "10", "1", "2", "3", "4", "5", "11", "1", "2", "3", "4", "6", "12", "1", "2", "3", "5", "6", "13", "1", "2", "3", "6", "7", "14", "1", "3", "7", "15", "1", "2", "3", "4", "7", "8", "15", "16", "1", "2", "3", "4", "6", "7", "8", "14", "17", "1", "2", "3", "4", "5", "6", "9", "13", "18" ]
[ "nonn", "base", "tabf" ]
11
1
3
[ "A165416", "A356148", "A356149", "A356150" ]
null
Rémy Sigrist, Jul 28 2022
2022-07-31T19:54:04
oeisdata/seq/A356/A356149.seq
217d81c9868f67d29efd581cb1cf0edd
A356150
a(n) is the sum of the positive integers whose binary expansion appears as a substring in the binary expansion of n or its complement.
[ "1", "3", "4", "10", "8", "12", "11", "25", "25", "18", "26", "28", "30", "33", "26", "56", "62", "61", "56", "56", "39", "63", "64", "67", "62", "66", "72", "77", "80", "78", "57", "119", "139", "143", "137", "135", "134", "119", "134", "134", "134", "81", "120", "138", "139", "147", "142", "146", "147", "148", "132", "153", "140", "157", "165", "165", "168", "174", "181" ]
[ "nonn", "base" ]
10
1
2
[ "A078823", "A356148", "A356149", "A356150" ]
null
Rémy Sigrist, Jul 28 2022
2022-07-31T19:54:18
oeisdata/seq/A356/A356150.seq
755a82f3cfc6b6caff1435c6da2774aa
A356151
Greatest common divisor of n and the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.
[ "1", "1", "1", "4", "5", "2", "7", "8", "3", "5", "11", "4", "13", "7", "5", "16", "17", "3", "19", "4", "7", "11", "23", "8", "5", "13", "9", "28", "29", "5", "31", "32", "11", "17", "7", "4", "37", "19", "13", "8", "41", "14", "43", "44", "5", "23", "47", "16", "7", "10", "17", "52", "53", "9", "11", "8", "19", "29", "59", "4", "61", "31", "21", "64", "13", "11", "67", "68", "23", "7", "71", "8", "73", "37", "5", "76", "11", "26", "79", "16", "27", "41", "83", "28", "17", "43", "29", "88" ]
[ "nonn" ]
11
1
4
[ "A276086", "A324580", "A355944", "A355945", "A356151", "A356152", "A356153" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T15:15:30
oeisdata/seq/A356/A356151.seq
75896598a2978697268a63f29bdde42c
A356152
Numerator of n / the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.
[ "1", "2", "3", "1", "1", "3", "1", "1", "3", "2", "1", "3", "1", "2", "3", "1", "1", "6", "1", "5", "3", "2", "1", "3", "5", "2", "3", "1", "1", "6", "1", "1", "3", "2", "5", "9", "1", "2", "3", "5", "1", "3", "1", "1", "9", "2", "1", "3", "7", "5", "3", "1", "1", "6", "5", "7", "3", "2", "1", "15", "1", "2", "3", "1", "5", "6", "1", "1", "3", "10", "1", "9", "1", "2", "15", "1", "7", "3", "1", "5", "3", "2", "1", "3", "5", "2", "3", "1", "1", "18", "7", "1", "3", "2", "5", "3", "1", "14", "9", "25", "1", "6", "1", "1", "15" ]
[ "nonn", "frac" ]
8
1
2
[ "A276086", "A324580", "A355944", "A355945", "A356151", "A356152", "A356153" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T15:15:33
oeisdata/seq/A356/A356152.seq
6f02927c42e9a3131e6fa113ff85323c
A356153
Denominator of n / the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.
[ "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "4", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "2", "1", "1", "1", "1", "5", "1", "3", "1", "1", "1", "1", "2" ]
[ "nonn", "frac" ]
9
1
3
[ "A276086", "A324580", "A355944", "A355945", "A356151", "A356152", "A356153", "A356154" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T15:15:37
oeisdata/seq/A356/A356153.seq
0ec4fd72b98458db4d12e2ea5f867d48
A356154
Dirichlet inverse of A356153.
[ "1", "-1", "-2", "0", "-1", "3", "-1", "0", "3", "1", "-1", "-1", "-1", "1", "3", "0", "-1", "-7", "-1", "-1", "2", "1", "-1", "0", "-1", "1", "-5", "0", "-1", "-5", "-1", "0", "3", "1", "1", "5", "-1", "1", "2", "2", "-1", "-3", "-1", "0", "-7", "1", "-1", "0", "-4", "2", "3", "0", "-1", "15", "1", "-3", "2", "1", "-1", "5", "-1", "1", "-3", "0", "1", "-5", "-1", "0", "3", "-1", "-1", "-2", "-1", "1", "2", "0", "-1", "-3", "-1", "-1", "8", "1", "-1", "1", "1", "1", "3", "0", "-1", "17" ]
[ "sign" ]
7
1
3
[ "A276086", "A355944", "A356151", "A356153", "A356154" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:15:56
oeisdata/seq/A356/A356154.seq
aec635d434e697dda2774969ab58504a
A356155
The pi-based arithmetic derivative applied to prime shift array: Square array A(n,k) = A258851(A246278(n,k)), read by falling antidiagonals.
[ "1", "4", "2", "7", "12", "3", "12", "19", "30", "4", "11", "54", "41", "56", "5", "20", "26", "225", "79", "110", "6", "15", "87", "58", "588", "131", "156", "7", "32", "37", "310", "94", "1815", "193", "238", "8", "33", "216", "69", "861", "162", "3042", "269", "304", "9", "32", "140", "1500", "117", "2156", "218", "6069", "355", "414", "10", "21", "120", "427", "5488", "183", "3835", "314", "8664", "491", "580", "11", "52", "44", "455", "1254", "26620", "255", "6834", "422", "14283", "629", "682", "12" ]
[ "nonn", "tabl" ]
12
1
2
[ "A000027", "A097240", "A246278", "A258851", "A344027", "A356155" ]
null
Antti Karttunen, Jul 29 2022
2022-07-31T08:15:31
oeisdata/seq/A356/A356155.seq
83fac72813197a63ee2f34125038c5ae
A356156
The nearest common ancestor of n and gcd(n, sigma(n)) in the Doudna tree (A005940).
[ "1", "1", "1", "1", "1", "6", "1", "1", "1", "2", "1", "2", "1", "2", "3", "1", "1", "2", "1", "2", "1", "2", "1", "12", "1", "2", "1", "28", "1", "6", "1", "1", "3", "2", "1", "1", "1", "2", "1", "10", "1", "3", "1", "2", "3", "2", "1", "2", "1", "1", "3", "2", "1", "2", "1", "2", "1", "2", "1", "6", "1", "2", "1", "1", "1", "3", "1", "2", "3", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "5", "1", "2", "3", "2", "1", "2", "5", "2", "1", "2", "5", "12", "1", "1", "3", "1", "1", "3", "1", "2", "3" ]
[ "nonn" ]
13
1
6
[ "A000203", "A007691", "A009194", "A347879", "A348040", "A348041", "A356156", "A356157", "A356158", "A356306" ]
null
Antti Karttunen, Jul 30 2022
2022-08-04T22:27:27
oeisdata/seq/A356/A356156.seq
ec8e52b76c1046d01b2c84f5fe590afc
A356157
The nearest common ancestor of sigma(n) and gcd(n, sigma(n)) in the Doudna tree (A005940).
[ "1", "1", "1", "1", "1", "6", "1", "1", "1", "2", "1", "2", "1", "2", "3", "1", "1", "3", "1", "2", "1", "2", "1", "6", "1", "2", "1", "28", "1", "2", "1", "1", "3", "2", "1", "1", "1", "2", "1", "3", "1", "6", "1", "2", "3", "2", "1", "2", "1", "1", "2", "2", "1", "6", "1", "2", "1", "2", "1", "3", "1", "2", "1", "1", "1", "2", "1", "2", "3", "2", "1", "3", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "28", "1", "2", "3", "2", "1", "2", "7", "2", "1", "2", "3", "3", "1", "1", "3", "1", "1", "2", "1", "2", "3" ]
[ "nonn" ]
11
1
6
[ "A000203", "A009194", "A336702", "A347879", "A348040", "A348041", "A356156", "A356157", "A356307" ]
null
Antti Karttunen, Jul 30 2022
2022-08-04T22:27:19
oeisdata/seq/A356/A356157.seq
d525ea9019337ac85091a6ec2860cade
A356158
a(n) = gcd(n, A347879(n)).
[ "1", "2", "1", "2", "1", "6", "1", "2", "1", "2", "1", "3", "1", "1", "3", "2", "1", "2", "1", "10", "1", "2", "1", "6", "1", "1", "1", "28", "1", "2", "1", "2", "3", "2", "1", "2", "1", "1", "1", "1", "1", "3", "1", "1", "3", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "3", "1", "1", "1", "2", "5", "2", "1", "1", "3", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "3", "1", "1", "3", "1", "1", "1", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "1", "3" ]
[ "nonn" ]
10
1
2
[ "A000203", "A336702", "A347879", "A348040", "A348041", "A356156", "A356157", "A356158", "A356308" ]
null
Antti Karttunen, Jul 30 2022
2022-08-04T22:27:14
oeisdata/seq/A356/A356158.seq
3ec488c65ccb586ee123da39ac8f5aeb
A356159
Sum of the prime indices of the smallest number that has the same prime signature as n.
[ "0", "1", "1", "2", "1", "3", "1", "3", "2", "3", "1", "4", "1", "3", "3", "4", "1", "4", "1", "4", "3", "3", "1", "5", "2", "3", "3", "4", "1", "6", "1", "5", "3", "3", "3", "6", "1", "3", "3", "5", "1", "6", "1", "4", "4", "3", "1", "6", "2", "4", "3", "4", "1", "5", "3", "5", "3", "3", "1", "7", "1", "3", "4", "6", "3", "6", "1", "4", "3", "6", "1", "7", "1", "3", "4", "4", "3", "6", "1", "6", "4", "3", "1", "7", "3", "3", "3", "5", "1", "7", "3", "4", "3", "3", "3", "7", "1", "4", "4", "6", "1", "6", "1", "5", "6" ]
[ "nonn" ]
13
1
4
[ "A046523", "A056239", "A355930", "A356159" ]
null
Antti Karttunen, Oct 25 2022
2022-10-30T23:05:35
oeisdata/seq/A356/A356159.seq
ca0721b9bb33e9ae1eb8d6036c8f3de9
A356160
Numbers k such that the smallest positive k such that n divides k*A276086(k) is equal to n, where A276086 is primorial base exp-function.
[ "1", "4", "5", "7", "8", "11", "13", "16", "17", "19", "23", "28", "29", "31", "32", "37", "41", "43", "44", "47", "52", "53", "59", "61", "64", "67", "68", "71", "73", "76", "79", "83", "88", "89", "92", "97", "101", "103", "104", "107", "108", "109", "113", "116", "121", "124", "127", "128", "131", "136", "137", "139", "143", "148", "149", "151", "152", "155", "157", "163", "164", "167", "169", "172", "173", "176", "179", "181", "184", "187", "188", "191" ]
[ "nonn" ]
6
1
2
[ "A276086", "A324580", "A324583", "A355944", "A355945", "A356160", "A356161" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T09:19:58
oeisdata/seq/A356/A356160.seq
ef4671c0b16a57cb609b78007a4b4724
A356161
a(n) = 1 if the smallest positive k such that n divides k*A276086(k) is equal to n, otherwise 0, where A276086 is primorial base exp-function.
[ "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1" ]
[ "nonn" ]
9
1
null
[ "A276086", "A324580", "A355944", "A355945", "A356160", "A356161" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T15:17:54
oeisdata/seq/A356/A356161.seq
acad38b5fbcf63019e5c54e8a3185b1a
A356162
a(n) = 1 if n and A276086(n) are coprime, otherwise 0, where A276086 is primorial base exp-function.
[ "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "1", "0", "1", "0", "1", "0", "1", "1" ]
[ "nonn" ]
9
0
null
[ "A276086", "A322585", "A324198", "A324583", "A324584", "A355820", "A356162" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T15:18:08
oeisdata/seq/A356/A356162.seq
9154d82cd8d124c4b7e6995e9708640f
A356163
a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0.
[ "1", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1" ]
[ "nonn" ]
32
1
null
[ "A000265", "A001414", "A003961", "A036349", "A065043", "A335657", "A353557", "A356163", "A359154", "A359773" ]
null
Antti Karttunen, Nov 02 2022
2025-03-23T03:20:48
oeisdata/seq/A356/A356163.seq
fdacd45d0e03ff0c9762c3c7241b543f
A356164
a(n) is the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
[ "1", "2", "2", "4", "3", "2", "5", "8", "4", "6", "7", "4", "11", "10", "3", "16", "13", "4", "17", "12", "10", "14", "19", "8", "9", "22", "8", "20", "23", "6", "29", "32", "14", "26", "5", "4", "31", "34", "22", "24", "37", "10", "41", "28", "6", "38", "43", "16", "25", "18", "26", "44", "47", "8", "21", "40", "34", "46", "53", "12", "59", "58", "20", "64", "33", "14", "61", "52", "38", "10", "67", "8", "71", "62", "9", "68", "7", "22", "73", "48", "16", "74", "79", "20", "39", "82" ]
[ "nonn" ]
14
1
2
[ "A000040", "A003961", "A191002", "A344005", "A355944", "A356164", "A356165", "A356166", "A356167", "A356168", "A356169" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:00
oeisdata/seq/A356/A356164.seq
a827c38d66daa15e4b282e08de280ef5
A356165
a(n) = n minus the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
[ "0", "0", "1", "0", "2", "4", "2", "0", "5", "4", "4", "8", "2", "4", "12", "0", "4", "14", "2", "8", "11", "8", "4", "16", "16", "4", "19", "8", "6", "24", "2", "0", "19", "8", "30", "32", "6", "4", "17", "16", "4", "32", "2", "16", "39", "8", "4", "32", "24", "32", "25", "8", "6", "46", "34", "16", "23", "12", "6", "48", "2", "4", "43", "0", "32", "52", "6", "16", "31", "60", "4", "64", "2", "12", "66", "8", "70", "56", "6", "32", "65", "8", "4", "64", "46", "4", "41", "32", "6", "84", "36" ]
[ "nonn" ]
12
1
5
[ "A000079", "A000720", "A001223", "A003961", "A191002", "A355945", "A356164", "A356165", "A356166" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:03
oeisdata/seq/A356/A356165.seq
de0de967cb56b89f0ce4c7c0979e0101
A356166
Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
[ "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "3", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "6", "1", "32", "1", "2", "5", "4", "1", "2", "1", "8", "1", "2", "1", "4", "3", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "12", "1", "2", "1", "64", "1", "2", "1", "4", "1", "10", "1", "8", "1", "2", "3", "4", "7", "2", "1", "16", "1", "2", "1", "4", "1", "2", "1", "8", "1", "6", "1", "4", "1", "2", "1", "32", "1", "2", "1", "4", "1", "2", "1", "8", "5" ]
[ "nonn", "look" ]
10
1
2
[ "A003961", "A191002", "A345992", "A356151", "A356164", "A356165", "A356166", "A356167", "A356168", "A356171", "A356172" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:07
oeisdata/seq/A356/A356166.seq
c3795de7d416d923f1f7de34cb825942
A356167
Greatest common divisor of A003961(n) and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "5", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "5", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "7", "1", "1", "1", "1", "3", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "5", "1", "1", "1", "1", "1", "3", "11", "1", "1", "1", "1", "1", "1", "1", "1", "9", "1", "1", "1", "1", "5" ]
[ "nonn", "look" ]
8
1
10
[ "A003961", "A191002", "A345993", "A356164", "A356165", "A356166", "A356167" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:10
oeisdata/seq/A356/A356167.seq
5c09cab28bae0e880abe191569567d43
A356168
Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).
[ "1", "1", "3", "1", "5", "3", "7", "1", "9", "5", "11", "3", "13", "7", "5", "1", "17", "9", "19", "5", "21", "11", "23", "3", "25", "13", "27", "7", "29", "15", "31", "1", "33", "17", "7", "9", "37", "19", "39", "5", "41", "21", "43", "11", "15", "23", "47", "3", "49", "25", "51", "13", "53", "27", "55", "7", "57", "29", "59", "15", "61", "31", "63", "1", "65", "33", "67", "17", "69", "7", "71", "9", "73", "37", "25", "19", "11", "39", "79", "5", "81", "41", "83", "21", "85", "43" ]
[ "nonn" ]
10
1
3
[ "A003961", "A356164", "A356166", "A356167", "A356168", "A356169" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:14
oeisdata/seq/A356/A356168.seq
16e0fe6970697a135c87edb075a296a7
A356169
a(n) = n - gcd(n, A003961(A356164(n))), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).
[ "0", "1", "0", "3", "0", "3", "0", "7", "0", "5", "0", "9", "0", "7", "10", "15", "0", "9", "0", "15", "0", "11", "0", "21", "0", "13", "0", "21", "0", "15", "0", "31", "0", "17", "28", "27", "0", "19", "0", "35", "0", "21", "0", "33", "30", "23", "0", "45", "0", "25", "0", "39", "0", "27", "0", "49", "0", "29", "0", "45", "0", "31", "0", "63", "0", "33", "0", "51", "0", "63", "0", "63", "0", "37", "50", "57", "66", "39", "0", "75", "0", "41", "0", "63", "0", "43", "0", "77", "0", "75", "0", "69" ]
[ "nonn" ]
10
1
4
[ "A003961", "A356164", "A356166", "A356168", "A356169", "A356171", "A356172" ]
null
Antti Karttunen, Jul 28 2022
2022-07-28T21:16:18
oeisdata/seq/A356/A356169.seq
59050c2b03cf489e346e882191df4375
A356170
a(n) = 1 if A001222(n) == 2*A007814(n), and otherwise 0, where A001222 is bigomega (number of prime factors with multiplicity) and A007814 is the 2-adic valuation of n.
[ "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1" ]
[ "nonn" ]
11
1
null
[ "A001222", "A007814", "A072978", "A356170" ]
null
Antti Karttunen, Nov 02 2022
2022-11-03T04:29:01
oeisdata/seq/A356/A356170.seq
f44f3b534b3c790b5f05e9b14fcf2c18
A356171
Odd numbers that are not divisible by two consecutive prime numbers.
[ "1", "3", "5", "7", "9", "11", "13", "17", "19", "21", "23", "25", "27", "29", "31", "33", "37", "39", "41", "43", "47", "49", "51", "53", "55", "57", "59", "61", "63", "65", "67", "69", "71", "73", "79", "81", "83", "85", "87", "89", "91", "93", "95", "97", "99", "101", "103", "107", "109", "111", "113", "115", "117", "119", "121", "123", "125", "127", "129", "131", "133", "137", "139", "141", "145", "147", "149", "151", "153", "155", "157", "159", "161", "163" ]
[ "nonn" ]
10
1
2
[ "A003961", "A319630", "A356164", "A356166", "A356169", "A356171", "A356172" ]
null
Antti Karttunen, Jul 28 2022
2022-07-29T09:52:52
oeisdata/seq/A356/A356171.seq
07b65a80cddd46ff48883dfa0af56e5b
A356172
a(n) = 1 if n is odd and not divisible by two consecutive prime numbers, otherwise 0.
[ "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1" ]
[ "nonn" ]
18
1
null
[ "A000035", "A003961", "A322361", "A356164", "A356166", "A356169", "A356171", "A356172", "A356173" ]
null
Antti Karttunen, Jul 28 2022
2022-07-29T09:53:00
oeisdata/seq/A356/A356172.seq
1f13e66a890aca1a516118b09341547f
A356173
a(n) = 1 if n is not divisible by two consecutive prime numbers, otherwise 0.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "1", "0", "1", "0", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1" ]
[ "nonn" ]
12
1
null
[ "A003961", "A296210", "A319630", "A322361", "A356172", "A356173" ]
null
Antti Karttunen, Jul 29 2022
2022-07-29T23:48:26
oeisdata/seq/A356/A356173.seq
258cc9e478cf6cd2dac71bd461b96ce3
A356174
Replace all prime factors p of n with n/p, then take the integer logarithm (A001414).
[ "0", "0", "0", "4", "0", "5", "0", "12", "6", "7", "0", "14", "0", "9", "8", "24", "0", "16", "0", "18", "10", "13", "0", "27", "10", "15", "18", "22", "0", "20", "0", "40", "14", "19", "12", "30", "0", "21", "16", "33", "0", "24", "0", "30", "22", "25", "0", "44", "14", "24", "20", "34", "0", "33", "16", "39", "22", "31", "0", "36", "0", "33", "26", "60", "18", "32", "0", "42", "26", "28", "0", "48", "0", "39" ]
[ "nonn" ]
28
1
4
[ "A000040", "A001222", "A001414", "A003415", "A014612", "A072195", "A328303", "A356174" ]
null
Thomas Scheuerle, Jul 28 2022
2022-07-31T13:59:31
oeisdata/seq/A356/A356174.seq
b70c3b766af4ace1a448d03d790decd0
A356175
Numbers k such that k^2 + {1,3,7,13,163} are prime.
[ "2", "4", "10", "14290", "64390", "74554", "83464", "93460", "132304", "238850", "262630", "277630", "300206", "352600", "376190", "404954", "415180", "610340", "806180", "984686", "1025650", "1047050", "1106116", "1382860", "2014624", "2440714", "2525870", "2538344", "2760026", "2826380", "3145600", "3508586", "3715156" ]
[ "nonn" ]
72
1
1
[ "A005574", "A049422", "A080149", "A113536", "A114270", "A182238", "A356109", "A356110", "A356175" ]
null
Jean-Marc Rebert, Jul 28 2022
2023-03-07T18:53:17
oeisdata/seq/A356/A356175.seq
c8a89b1a797d4ffc3d790a363bc0f8ab
A356176
Numbers that can be written as the product of three divisors greater than 1 such that the number in binary is contained in the string concatenation of the divisors in binary.
[ "30", "60", "63", "90", "110", "120", "126", "180", "220", "228", "240", "252", "340", "350", "430", "440", "480", "495", "504", "606", "612", "680", "759", "840", "860", "880", "891", "927", "957", "960", "990", "1008", "1212", "1224", "1320", "1526", "1710", "1720", "1755", "1760", "1782", "1854", "1920", "1980", "2016", "2376", "2424", "2466", "2640", "2925", "2955", "2990", "3045", "3050" ]
[ "nonn", "base" ]
10
1
1
[ "A027750", "A030190", "A210959", "A355790", "A355791", "A355852", "A355857", "A356143", "A356176" ]
null
Scott R. Shannon, Jul 28 2022
2022-07-30T14:14:41
oeisdata/seq/A356/A356176.seq
1938c75af05b138298588ac69d413495
A356177
Palindromes in A333369.
[ "1", "3", "5", "7", "9", "22", "44", "66", "88", "111", "212", "232", "252", "272", "292", "333", "414", "434", "454", "474", "494", "555", "616", "636", "656", "676", "696", "777", "818", "838", "858", "878", "898", "999", "2002", "2222", "2442", "2662", "2882", "4004", "4224", "4444", "4664", "4884", "6006", "6226", "6446", "6666", "6886", "8008", "8228", "8448", "8668", "8888", "10101" ]
[ "nonn", "base" ]
29
1
2
[ "A002113", "A100706", "A333369", "A355770", "A355771", "A355772", "A356177" ]
null
Bernard Schott, Jul 28 2022
2022-07-30T12:59:57
oeisdata/seq/A356/A356177.seq
a4162d6e7b1c21936770e6af91641d24
A356178
Numbers k such that both Sum_{i=1..k} i*prime(i) and Sum_{i=1..k} (k+1-i)*prime(i) are prime.
[ "1", "3", "199", "351", "1583", "1955", "2579", "2627", "3251", "3407", "3503", "5311", "6359", "6819", "7295", "7547", "8791", "9663", "10143", "10591", "11499", "11579", "12199", "12443", "14527", "15563", "15583", "16051", "16543", "16655", "18047", "18319", "20691", "20847", "23979", "24079", "24575", "25667", "26491", "28235", "30395", "30627", "32235", "32259", "33091", "33287", "33527" ]
[ "nonn" ]
13
1
2
[ "A014148", "A014285", "A356178" ]
null
J. M. Bergot and Robert Israel, Jul 28 2022
2022-08-03T12:40:18
oeisdata/seq/A356/A356178.seq
ca4126c8ab425eef3c51d7795aae5277
A356179
Positions of records in A279497, i.e., integers whose number of pentagonal divisors sets a new record.
[ "1", "5", "35", "70", "210", "420", "2310", "4620", "18480", "32340", "60060", "120120", "240240", "720720", "1141140", "2042040", "4084080", "4564560", "13693680", "19399380", "38798760", "77597520", "232792560", "387987600" ]
[ "nonn", "more" ]
19
1
2
[ "A000326", "A046952", "A093036", "A279497", "A350756", "A355595", "A356132", "A356179" ]
null
Bernard Schott, Jul 28 2022
2022-07-30T08:20:36
oeisdata/seq/A356/A356179.seq
8d46ff8702c579d429c49f8aa979e557
A356180
a(n) = A022838(A001951(n)).
[ "1", "3", "6", "8", "12", "13", "15", "19", "20", "24", "25", "27", "31", "32", "36", "38", "41", "43", "45", "48", "50", "53", "55", "57", "60", "62", "65", "67", "71", "72", "74", "77", "79", "83", "84", "86", "90", "91", "95", "96", "98", "102", "103", "107", "109", "112", "114", "116", "119", "121", "124", "126", "128", "131", "133", "136", "138", "142", "143", "145", "148" ]
[ "nonn", "easy" ]
12
1
2
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356180", "A356181", "A356182", "A356183" ]
null
Clark Kimberling, Aug 24 2022
2023-06-05T08:56:02
oeisdata/seq/A356/A356180.seq
76aa6a84751673b214aa70702781ada4
A356181
a(n) = A054406(A001951(n)).
[ "2", "4", "9", "11", "16", "18", "21", "26", "28", "33", "35", "37", "42", "44", "49", "52", "56", "59", "61", "66", "68", "73", "75", "78", "82", "85", "89", "92", "97", "99", "101", "106", "108", "113", "115", "118", "123", "125", "130", "132", "134", "139", "141", "146", "149", "153", "156", "158", "163", "165", "170", "172", "175", "179", "182", "186", "189", "194" ]
[ "nonn", "easy" ]
7
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356180", "A356181", "A356182", "A356183" ]
null
Clark Kimberling, Aug 24 2022
2025-03-23T18:39:38
oeisdata/seq/A356/A356181.seq
ff9a0e5080e747874a2da04b4ed720a2
A356182
a(n) = A022838(A001952(n)).
[ "5", "10", "17", "22", "29", "34", "39", "46", "51", "58", "64", "69", "76", "81", "88", "93", "100", "105", "110", "117", "122", "129", "135", "140", "147", "152", "159", "164", "171", "176", "181", "188", "193", "200", "206", "211", "218", "223", "230", "235", "240", "247", "252", "259", "265", "271", "277", "282", "289", "294", "301", "306", "311", "318", "323" ]
[ "nonn", "easy" ]
11
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356180", "A356181", "A356182", "A356183" ]
null
Clark Kimberling, Aug 24 2022
2025-03-23T18:40:03
oeisdata/seq/A356/A356182.seq
03121bea1701234d9fd85325d9f66f1b
A356183
a(n) = A054406(A001952(n)).
[ "7", "14", "23", "30", "40", "47", "54", "63", "70", "80", "87", "94", "104", "111", "120", "127", "137", "144", "151", "160", "167", "177", "184", "191", "201", "208", "217", "224", "234", "241", "248", "257", "264", "274", "281", "288", "298", "305", "314", "321", "328", "338", "345", "354", "362", "371", "378", "385", "395", "402", "411", "418", "425", "435" ]
[ "nonn", "easy" ]
7
1
1
[ "A001951", "A001952", "A022838", "A054406", "A346308", "A356088", "A356180", "A356181", "A356182", "A356183" ]
null
Clark Kimberling, Aug 24 2022
2025-03-23T18:39:58
oeisdata/seq/A356/A356183.seq
0bb0309822067e132e46649ab18894aa
A356184
Triangle read by rows: n-th row gives the indices of the n repunits that divide A340549(n).
[ "1", "1", "2", "1", "2", "4", "1", "2", "3", "6", "1", "2", "3", "4", "6", "1", "2", "3", "4", "6", "12", "1", "2", "3", "4", "6", "8", "12", "1", "2", "3", "4", "5", "6", "10", "12", "1", "2", "3", "4", "5", "6", "8", "10", "12", "1", "2", "3", "4", "5", "6", "8", "9", "10", "12", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "15", "18", "20", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "15", "18", "20", "24" ]
[ "nonn", "base", "tabl" ]
22
1
3
[ "A002275", "A004023", "A083230", "A340549", "A356184" ]
null
Bernard Schott, Jul 28 2022
2022-09-12T11:42:17
oeisdata/seq/A356/A356184.seq
dadb7aedd97cfbb9472f6873b24f85d4
A356185
The difference between number of even and number of odd Grassmannian permutations of size n.
[ "1", "1", "0", "1", "0", "3", "2", "9", "8", "23", "22", "53", "52", "115", "114", "241", "240", "495", "494", "1005", "1004", "2027", "2026", "4073", "4072", "8167", "8166", "16357", "16356", "32739", "32738", "65505", "65504", "131039", "131038", "262109", "262108", "524251", "524250", "1048537", "1048536", "2097111", "2097110", "4194261", "4194260" ]
[ "nonn", "easy" ]
30
0
6
[ "A000325", "A001710", "A005803", "A032085", "A060546", "A122746", "A183155", "A233411", "A356185" ]
null
Per W. Alexandersson, Jul 28 2022
2022-07-30T11:44:35
oeisdata/seq/A356/A356185.seq
c46459d339a75ced91a640a21038f9fd
A356186
Number of labeled trees on [2n] with a bicentroid.
[ "0", "1", "12", "810", "143360", "49218750", "27935373312", "23751648836916", "28301429298954240", "45046920790988254710", "92378000000000000000000", "237289687212632836205339916", "746430126201849206626773368832", "2822726846177838977566127355808300" ]
[ "nonn" ]
46
0
3
[ "A000169", "A000984", "A102911", "A356186" ]
null
Geoffrey Critzer, Jul 31 2022
2022-07-31T19:52:48
oeisdata/seq/A356/A356186.seq
c52418c23dd97727d06c7fd8446cc69c
A356187
Number of permutations f of {1,...,n} with f(1) = 1 such that those k*f(k) + 1 (k = 1..n) are n distinct primes.
[ "1", "1", "0", "0", "0", "2", "2", "6", "4", "24", "6", "162", "330", "1428", "1632" ]
[ "nonn", "more" ]
19
1
6
[ "A000040", "A321597", "A333083", "A356187" ]
null
Zhi-Wei Sun, Jul 28 2022
2022-08-06T08:07:22
oeisdata/seq/A356/A356187.seq
d2bbb99765dca6fe61561f6a1efeb41e
A356188
a(1)=1; for n > 1, if a(n-1) is prime then a(n) = the smallest number not yet in the sequence. Otherwise a(n) = a(n-1) + n - 1.
[ "1", "2", "3", "4", "8", "13", "5", "6", "14", "23", "7", "9", "21", "34", "48", "63", "79", "10", "28", "47", "11", "12", "34", "57", "81", "106", "132", "159", "187", "216", "246", "277", "15", "48", "82", "117", "153", "190", "228", "267", "307", "16", "58", "101", "17", "18", "64", "111", "159", "208", "258", "309", "361", "414", "468", "523", "19", "20", "78", "137", "22", "83", "24", "87", "151", "25", "91" ]
[ "nonn", "easy" ]
19
1
2
[ "A000040", "A060735", "A073659", "A331603", "A356188" ]
null
John Tyler Rascoe, Jul 28 2022
2022-09-28T08:13:21
oeisdata/seq/A356/A356188.seq
bc1ee28d2cc57c554dbdd73c5c24c83b
A356189
Optimal link functions for repeat avoidance in double elimination tournaments.
[ "0", "2", "0", "4", "24", "56", "64", "160", "192", "448", "256", "2816", "1536", "3584", "18432", "47104", "77824", "159744", "385024", "163840", "360448", "3932160", "8126464", "16515072", "6029312", "63963136", "128974848", "266338304", "524288000", "1069547520", "2071986176", "4211081216", "8438939648", "16240345088", "32614907904", "65364033536" ]
[ "nonn" ]
45
1
2
null
null
Chris Shaw, Jul 28 2022
2023-11-28T01:09:03
oeisdata/seq/A356/A356189.seq
3a6bd843fd18caafe46093f23fb4fc11
A356190
a(n) is the least prime p such that there are exactly n primes strictly between p and 2*p, or -1 if there is no such p.
[ "2", "7", "11", "17", "23", "29", "31", "-1", "37", "-1", "53", "61", "59", "71", "79", "89", "-1", "109", "97", "101", "-1", "-1", "127", "-1", "137", "151", "149", "157", "-1", "179", "-1", "191", "-1", "-1", "211", "-1", "-1", "223", "233", "-1", "251", "257", "263", "293", "-1", "-1", "-1", "-1", "307", "311", "-1", "-1", "-1", "331", "349", "347", "367", "373", "379", "389", "409", "-1", "-1", "419", "-1", "431", "443" ]
[ "sign" ]
9
1
1
[ "A168421", "A356190" ]
null
J. M. Bergot and Robert Israel, Jul 29 2022
2022-08-18T11:44:32
oeisdata/seq/A356/A356190.seq
b37df222b9481296e912dac2806da699
A356191
a(n) is the smallest exponentially odd number that is divisible by n.
[ "1", "2", "3", "8", "5", "6", "7", "8", "27", "10", "11", "24", "13", "14", "15", "32", "17", "54", "19", "40", "21", "22", "23", "24", "125", "26", "27", "56", "29", "30", "31", "32", "33", "34", "35", "216", "37", "38", "39", "40", "41", "42", "43", "88", "135", "46", "47", "96", "343", "250", "51", "104", "53", "54", "55", "56", "57", "58", "59", "120", "61", "62", "189", "128", "65" ]
[ "nonn", "easy", "mult" ]
14
1
2
[ "A007913", "A053143", "A053149", "A053167", "A064549", "A066638", "A087320", "A087321", "A197863", "A268335", "A336643", "A350390", "A356191", "A356192", "A356193", "A356194" ]
null
Amiram Eldar, Jul 29 2022
2023-09-09T07:42:39
oeisdata/seq/A356/A356191.seq
68e21a791a92618b6fdb017eee66110c
A356192
a(n) is the smallest cubefull exponentially odd number (A335988) that is divisible by n.
[ "1", "8", "27", "8", "125", "216", "343", "8", "27", "1000", "1331", "216", "2197", "2744", "3375", "32", "4913", "216", "6859", "1000", "9261", "10648", "12167", "216", "125", "17576", "27", "2744", "24389", "27000", "29791", "32", "35937", "39304", "42875", "216", "50653", "54872", "59319", "1000", "68921", "74088", "79507", "10648", "3375", "97336" ]
[ "nonn", "easy", "mult" ]
17
1
2
[ "A001694", "A013664", "A053143", "A053149", "A053167", "A066638", "A087320", "A087321", "A197863", "A268335", "A335988", "A356191", "A356192", "A356193", "A356194" ]
null
Amiram Eldar, Jul 29 2022
2022-11-13T08:40:51
oeisdata/seq/A356/A356192.seq
fe5729cc2ac21281433f210536d0eff9
A356193
a(n) is the smallest cubefull number (A036966) that is a multiple of n.
[ "1", "8", "27", "8", "125", "216", "343", "8", "27", "1000", "1331", "216", "2197", "2744", "3375", "16", "4913", "216", "6859", "1000", "9261", "10648", "12167", "216", "125", "17576", "27", "2744", "24389", "27000", "29791", "32", "35937", "39304", "42875", "216", "50653", "54872", "59319", "1000", "68921", "74088", "79507", "10648", "3375", "97336" ]
[ "nonn", "easy", "mult" ]
18
1
2
[ "A002117", "A036966", "A053143", "A053149", "A053167", "A066638", "A087320", "A087321", "A197863", "A356191", "A356192", "A356193", "A356194", "A360541" ]
null
Amiram Eldar, Jul 29 2022
2023-09-01T02:55:25
oeisdata/seq/A356/A356193.seq
3f818e0512cc5952aeb03f35a14bc38c
A356194
a(n) is the smallest multiple of n whose prime factorization exponents are all powers of 2.
[ "1", "2", "3", "4", "5", "6", "7", "16", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "48", "25", "26", "81", "28", "29", "30", "31", "256", "33", "34", "35", "36", "37", "38", "39", "80", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "162", "55", "112", "57", "58", "59", "60", "61", "62", "63", "256", "65", "66", "67" ]
[ "nonn", "easy", "mult" ]
10
1
2
[ "A053143", "A053149", "A053167", "A066638", "A087320", "A087321", "A138302", "A197863", "A353897", "A356191", "A356192", "A356193", "A356194" ]
null
Amiram Eldar, Jul 29 2022
2022-07-31T07:46:36
oeisdata/seq/A356/A356194.seq
0596c2f00b11e9955f9cc537e2676a4f
A356195
The binary expansion of a(n) is obtained by applying the totalistic cellular automaton with rule 2*n to the binary expansion of n.
[ "0", "1", "0", "3", "0", "6", "3", "7", "0", "14", "3", "14", "0", "9", "7", "15", "0", "30", "3", "30", "0", "25", "7", "30", "0", "16", "12", "29", "7", "23", "15", "31", "0", "62", "3", "62", "0", "57", "7", "62", "0", "48", "12", "61", "7", "55", "15", "62", "0", "32", "28", "60", "7", "38", "28", "61", "0", "33", "19", "51", "15", "47", "31", "63", "0", "126", "3", "126", "0", "121", "7", "126" ]
[ "nonn", "base" ]
13
0
4
[ "A000120", "A000225", "A038573", "A352528", "A356195", "A356215" ]
null
Rémy Sigrist, Jul 29 2022
2022-07-31T19:54:25
oeisdata/seq/A356/A356195.seq
b3ad6965095b6437213891435396a082
A356196
Consider pairs of consecutive primes {p,q} such that p, q, q-p and q+p all with distinct digits. Sequence gives lesser primes p.
[ "2", "3", "5", "13", "17", "19", "23", "29", "31", "37", "41", "43", "59", "61", "67", "73", "79", "83", "89", "103", "107", "137", "157", "167", "173", "193", "239", "241", "251", "257", "263", "269", "281", "283", "359", "389", "397", "401", "419", "421", "457", "461", "463", "467", "487", "523", "601", "613", "617", "619", "641", "643", "683" ]
[ "nonn", "base", "fini", "full" ]
52
1
1
[ "A029743", "A356196" ]
null
Zak Seidov, Oct 31 2022
2022-11-14T00:37:39
oeisdata/seq/A356/A356196.seq
ff9e266001e19eeaf83c5a1110cd0365
A356197
Number of Baxter 3-permutations of length n.
[ "1", "1", "4", "28", "260", "2872", "35620", "479508" ]
[ "nonn", "more" ]
8
0
3
[ "A001181", "A356197" ]
null
Nicolas Bonichon, Jul 29 2022
2022-09-27T19:35:53
oeisdata/seq/A356/A356197.seq
f2b1def5a0ffef4320da25361fa56302
A356198
Number of edge covers in the n-book graph.
[ "5", "41", "233", "1217", "6185", "31121", "155993", "780737", "3905225", "19529201", "97652153", "488273057", "2441389865", "12206998481", "61035090713", "305175650177", "1525878644105", "7629394006961", "38146971607673", "190734861184097", "953674312211945", "4768371573642641" ]
[ "nonn", "easy" ]
13
1
1
[ "A005057", "A016127", "A356198" ]
null
Eric W. Weisstein, Jul 29 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356198.seq
ec59b425df744f184b22d3f78edf992c
A356199
a(n) = Sum_{k=0..n} (n*k+1)^(k-1) * Stirling2(n,k).
[ "1", "1", "6", "122", "5991", "556152", "84245291", "18956006323", "5940695613628", "2474958812797662", "1323229303771318595", "883245295259143164922", "719968321620942410875645", "703829776430361739799683993", "812798413118207226439408790038", "1094718407894086754989907938078190" ]
[ "nonn" ]
22
0
3
[ "A000110", "A008277", "A048993", "A052880", "A349524", "A349525", "A349583", "A349654", "A349655", "A356199" ]
null
Alois P. Heinz, Jul 29 2022
2023-02-14T07:41:19
oeisdata/seq/A356/A356199.seq
8519da65459630ef380c4dd237d3b10b
A356200
Number of edge covers in the n-gear graph.
[ "3", "25", "162", "969", "5613", "32062", "181989", "1030017", "5821902", "32886505", "185714829", "1048619646", "5920559661", "33426829321", "188721717102", "1065481514817", "6015458406741", "33961820796094", "191740095366885", "1082517159435249", "6111623364952302", "34504707439240921" ]
[ "nonn", "easy" ]
17
1
1
null
null
Eric W. Weisstein, Jul 29 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356200.seq
eb8afde0861e43bd8b1e81c3373d27a1