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1999-12-11 03:00:00
2025-04-28 00:58:08
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A378501
Integers m such that A379816(m) = A379815(m) + m.
[ "3", "5", "6", "7", "10", "11", "13", "14", "15", "17", "19", "21", "22", "23", "24", "26", "27", "28", "29", "30", "31", "33", "34", "35", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "49", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79", "82", "83", "85", "86", "87" ]
[ "nonn" ]
14
1
1
[ "A378501", "A379815", "A379816", "A380743" ]
null
Michel Marcus, Feb 10 2025
2025-02-12T01:50:01
oeisdata/seq/A378/A378501.seq
17495cb61beeea1abaad63c3f86869cd
A378502
a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 3,2,0.
[ "1", "7", "30", "120", "483", "1934", "7736", "30947", "123790", "495160", "1980643", "7922574", "31690296", "126761187", "507044750", "2028179000", "8112716003", "32450864014", "129803456056", "519213824227", "2076855296910", "8307421187640", "33229684750563", "132918739002254", "531674956009016" ]
[ "nonn", "base", "easy" ]
25
1
2
[ "A037618", "A037667", "A378497", "A378499", "A378502" ]
null
Jonathan Shadrach Gilbert, Dec 03 2024
2024-12-21T00:20:36
oeisdata/seq/A378/A378502.seq
9bcb7ea8b40567860c51a60df596a174
A378503
Expansion of (Sum_{k>=0} binomial(4*k,k) * x^k)^3.
[ "1", "12", "132", "1396", "14436", "147120", "1483996", "14854968", "147821604", "1464031120", "14443875984", "142042418004", "1393053544508", "13630170286224", "133092301736232", "1297274743175856", "12624909478998948", "122692158505386960", "1190859983017752880", "11545524234978791952", "111820579340839270416" ]
[ "nonn" ]
13
0
2
[ "A002457", "A005810", "A078995", "A337291", "A378483", "A378484", "A378503" ]
null
Seiichi Manyama, Nov 28 2024
2024-11-29T08:12:18
oeisdata/seq/A378/A378503.seq
fbd2a2ec8d08252bdc0e90bedd174b72
A378504
Expansion of (Sum_{k>=0} binomial(3*k,k) * x^k)^4.
[ "1", "12", "114", "984", "8055", "63744", "492702", "3742704", "28053423", "208057260", "1529802648", "11168142048", "81041199876", "585045970992", "4204705925670", "30101448952032", "214756404746031", "1527491122906212", "10834911076417458", "76666402505673720", "541277205506059743" ]
[ "nonn" ]
9
0
2
[ "A002697", "A005809", "A006256", "A378483", "A378484", "A378504" ]
null
Seiichi Manyama, Nov 28 2024
2024-11-29T08:10:31
oeisdata/seq/A378/A378504.seq
3c1a4751d14e42e0ee64426416f15bd6
A378505
a(0) = 0, a(n) = 0 where a(n-1) is nonzero and divisible by n. Otherwise a(n) = n + a(n-1).
[ "0", "1", "3", "0", "4", "9", "15", "22", "30", "39", "49", "60", "0", "13", "27", "42", "58", "75", "93", "112", "132", "153", "175", "198", "222", "247", "273", "300", "328", "357", "387", "418", "450", "483", "517", "552", "588", "625", "663", "0", "40", "81", "123", "166", "210", "255", "301", "348", "396", "445", "495", "546", "598", "651", "705", "760", "816" ]
[ "nonn", "easy", "look" ]
49
0
3
[ "A068627", "A378505", "A379013" ]
null
Stuart Coe, Nov 29 2024
2024-12-13T14:51:01
oeisdata/seq/A378/A378505.seq
80c053f33b4e5f38fbf945be377dc87f
A378506
The number of solutions to the equation phi(phi(x)) = n, where phi is the Euler totient function.
[ "5", "8", "0", "13", "0", "4", "0", "23", "0", "2", "0", "14", "0", "0", "0", "36", "0", "2", "0", "5", "0", "2", "0", "32", "0", "0", "0", "2", "0", "0", "0", "54", "0", "0", "0", "11", "0", "0", "0", "23", "0", "0", "0", "5", "0", "0", "0", "66", "0", "0", "0", "2", "0", "4", "0", "3", "0", "0", "0", "2", "0", "0", "0", "78", "0", "0", "0", "0", "0", "0", "0", "38", "0", "0", "0", "0", "0", "0", "0", "41", "0", "2", "0", "6" ]
[ "nonn", "easy" ]
8
1
1
[ "A000010", "A010554", "A014197", "A378506", "A378507", "A378508" ]
null
Amiram Eldar, Nov 29 2024
2024-11-30T06:26:20
oeisdata/seq/A378/A378506.seq
b15a643168a47504d307f923e6a6afb6
A378507
The smallest number k such that the equation phi(phi(x)) = k has exactly n solutions.
[ "10", "56", "6", "1", "84", "312", "2", "200", "464", "36", "108", "4", "12", "88", "816", "264", "440", "360", "552", "120", "224", "8", "3696", "1320", "928", "176", "624", "1472", "832", "5728", "24", "4560", "1080", "2000", "16", "2848", "72", "1312", "1872", "80", "1120", "216", "880", "336", "23360", "448", "3808", "10608", "648", "528", "352", "9280", "32" ]
[ "nonn", "changed" ]
13
2
1
[ "A000010", "A007374", "A010554", "A378506", "A378507" ]
null
Amiram Eldar, Nov 29 2024
2025-04-26T06:00:29
oeisdata/seq/A378/A378507.seq
514f3421545161b663a9177b108f5837
A378508
Values taken by phi(phi(m)) (A010554).
[ "1", "2", "4", "6", "8", "10", "12", "16", "18", "20", "22", "24", "28", "32", "36", "40", "44", "48", "52", "54", "56", "60", "64", "72", "80", "82", "84", "88", "92", "96", "100", "104", "108", "112", "120", "128", "130", "132", "144", "156", "160", "162", "164", "168", "172", "176", "178", "180", "184", "190", "192", "200", "204", "208", "212", "216", "220", "224", "232", "238", "240", "250", "252", "256", "260", "264", "272", "276", "280", "288", "292", "300", "312", "320", "324", "328", "336", "344", "348", "352", "356", "358", "360", "368", "380", "384", "396", "400" ]
[ "nonn" ]
8
1
2
[ "A000010", "A002202", "A010554", "A378506", "A378508" ]
null
Amiram Eldar, Nov 29 2024
2024-11-30T06:26:10
oeisdata/seq/A378/A378508.seq
1b5d709039db338676668d34c919bce6
A378509
Totient numbers k for which there is no solution to the equation phi(phi(x)) = k.
[ "30", "42", "46", "58", "66", "70", "78", "102", "106", "110", "116", "126", "136", "138", "140", "148", "150", "166", "196", "198", "210", "222", "226", "228", "262", "268", "270", "282", "294", "296", "306", "310", "316", "330", "332", "342", "346", "366", "372", "378", "382", "388", "392", "438", "444", "452", "456", "460", "462", "466", "478", "498", "502", "506" ]
[ "nonn" ]
8
1
1
[ "A000010", "A002202", "A010554", "A378508", "A378509", "A378510" ]
null
Amiram Eldar, Nov 29 2024
2024-11-30T06:26:06
oeisdata/seq/A378/A378509.seq
7014344993d715748643ec02dbb33703
A378510
The least totient number k with exactly n solutions to the equation phi(x) = k, where all the solutions are nontotient numbers (A007617).
[ "30", "116", "42", "456", "780", "1140", "1368", "1380", "3420", "4356", "5104", "20196", "9396", "1980", "15876", "8316", "4860", "16380", "79464", "239976", "15720", "69300", "129960", "70000", "90360", "141680", "263160", "835380", "802296", "706680", "236808", "39960", "205800", "2898840", "3200904", "598920", "664440", "2723400" ]
[ "nonn" ]
11
2
1
[ "A000010", "A002202", "A007374", "A007617", "A014197", "A378509", "A378510" ]
null
Amiram Eldar, Nov 29 2024
2024-11-30T06:26:35
oeisdata/seq/A378/A378510.seq
a6681ad1db2d80fd8d2d4da947268e5f
A378511
Number of partitions of the repunit A002275(n) into two mutually complementary binary vectors having a common divisor > 1 in base 10.
[ "1", "0", "1", "1", "4", "1", "20", "1", "48", "85", "142", "1", "1136", "131", "1780", "6184", "9920", "1", "75434", "1", "124468", "369142", "429508", "1", "4797008", "416966", "6114994", "22482400", "28867896", "111651", "306153842", "384525", "507438240", "1483501078", "1242075014", "743845629", "19710473036", "34300", "17721793660" ]
[ "nonn", "base" ]
45
0
5
[ "A002275", "A004023", "A007088", "A378154", "A378511", "A378514", "A378761" ]
null
Dmytro Inosov, Nov 29 2024
2024-12-21T11:08:04
oeisdata/seq/A378/A378511.seq
f85491004a321c2ec812470cea56cb6e
A378512
Numbers k such that 6^sigma(k) - k is a prime.
[ "1", "7", "13", "77", "395", "2867", "3959", "5023" ]
[ "nonn", "more" ]
8
1
2
[ "A000043", "A000203", "A000668", "A023194", "A023195", "A253850", "A253851", "A367460", "A368651", "A377786", "A377927", "A378512" ]
null
J.W.L. (Jan) Eerland, Nov 29 2024
2024-12-21T00:49:04
oeisdata/seq/A378/A378512.seq
91a2b53c0f3888f7e9bd8e222646dd61
A378513
a(1) = 1, a(n) = a(n-1) + n if all the digits of a(n-1) do not share a divisor greater than 1. Otherwise, a(n) = a(n-1) divided by the gcd of all its individual digits.
[ "1", "3", "1", "5", "1", "7", "1", "9", "1", "11", "22", "11", "24", "12", "27", "43", "60", "10", "29", "49", "70", "10", "33", "11", "36", "12", "39", "13", "42", "21", "52", "84", "21", "55", "11", "47", "84", "21", "60", "10", "51", "93", "31", "75", "120", "166", "213", "261", "310", "360", "120", "172", "225", "279", "334", "390", "130", "188", "247", "307", "368", "430" ]
[ "nonn", "base", "look" ]
15
1
2
[ "A052423", "A378513" ]
null
Stuart Coe, Nov 29 2024
2024-12-17T13:02:02
oeisdata/seq/A378/A378513.seq
ff8ebadbe90907f8df093e0f3e38aed9
A378514
Number of partitions of 2^n-1 into two summands >= 0 having a common divisor > 1.
[ "0", "1", "1", "4", "1", "14", "1", "64", "40", "212", "56", "1184", "1", "2900", "2884", "16384", "1", "61088", "1", "284288", "159520", "776800", "89264", "5070848", "577216", "11195732", "10375168", "67834880", "1522240", "269570912", "1", "1073741824", "813199072", "2863486292", "917553184", "21299044352", "308159200", "45813683540" ]
[ "nonn" ]
52
1
4
[ "A000010", "A000043", "A000079", "A000225", "A000668", "A056742", "A082023", "A378511", "A378514" ]
null
Dmytro Inosov, Nov 29 2024
2024-11-30T08:50:40
oeisdata/seq/A378/A378514.seq
72bc215de6c90f53c0abd5bf5f0c6d58
A378515
Smallest n-digit number whose digits can be divided into an even number of substrings s_i (where i <= n) such that the sum of s_j^s_k (where j <= n and k <= n), with each substring used only once, equals the number k itself, or -1 if no such number exists.
[ "25", "-1", "4096", "15626", "117650", "1015626", "10077696", "100015628" ]
[ "sign", "base", "more" ]
54
2
1
[ "A004248", "A377012", "A378515" ]
null
Jean-Marc Rebert, Nov 29 2024
2024-12-12T23:30:47
oeisdata/seq/A378/A378515.seq
9d7345dc2e0d86f079d71aa90694b655
A378516
Number of dominating unique simple graphs on n nodes.
[ "1", "2", "4", "9", "21", "52", "168", "666", "3605", "27513" ]
[ "nonn", "more" ]
10
1
2
[ "A000088", "A378516", "A378517" ]
null
Eric W. Weisstein, Nov 29 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378516.seq
b6a86e93d2dd52b50e0c146f2fcf7389
A378517
Number of dominating nonunique simple graphs on n nodes.
[ "0", "0", "0", "2", "13", "104", "876", "11680", "271063", "11977655" ]
[ "nonn", "more" ]
10
1
4
[ "A000088", "A378516", "A378517" ]
null
Eric W. Weisstein, Nov 29 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378517.seq
ecfb5ec9bb7f15bb78ecdb8df6bbc2ab
A378518
a(n) = n - A019565(A048675(n)), where A019565 and A048675 are base-2 exp and log-functions.
[ "0", "0", "0", "1", "0", "0", "0", "2", "4", "0", "0", "7", "0", "0", "0", "11", "0", "8", "0", "5", "0", "0", "0", "14", "18", "0", "12", "7", "0", "0", "0", "22", "0", "0", "0", "21", "0", "0", "0", "10", "0", "0", "0", "11", "38", "0", "0", "33", "38", "36", "0", "13", "0", "24", "0", "14", "0", "0", "0", "53", "0", "0", "28", "49", "0", "0", "0", "17", "0", "0", "0", "42", "0", "0", "54", "19", "0", "0", "0", "73", "74", "0", "0", "49", "0", "0", "0", "22", "0", "76", "0", "23", "0", "0", "0", "66", "0", "76" ]
[ "nonn" ]
11
1
8
[ "A005117", "A019565", "A048675", "A097246", "A097248", "A376406", "A376417", "A376418", "A378518" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T21:04:32
oeisdata/seq/A378/A378518.seq
d8cb3cdba7093d64f2d9cc1fafc74698
A378519
Numbers which can be written in precisely one way as sum of a subset of their proper divisors but are not Zumkeller numbers, i.e., have no subsets of their divisors such that the complement has the same sum.
[ "748", "7544", "10184", "61904", "66928" ]
[ "nonn", "more" ]
9
1
1
[ "A064771", "A083210", "A376879", "A378519", "A378604" ]
null
Antti Karttunen, Dec 01 2024
2024-12-02T08:18:42
oeisdata/seq/A378/A378519.seq
4a3f9fd83f8f005060c5202f4697adcb
A378520
Dirichlet inverse of A336840, where A336840 is the inverse Möbius transform of A048673.
[ "1", "-3", "-4", "1", "-5", "10", "-7", "-1", "-1", "12", "-8", "-2", "-10", "16", "14", "-2", "-11", "5", "-13", "-2", "18", "18", "-16", "6", "-5", "22", "-8", "-2", "-17", "-20", "-20", "-4", "20", "24", "20", "1", "-22", "28", "24", "8", "-23", "-20", "-25", "-2", "11", "34", "-28", "14", "-19", "18", "26", "-2", "-31", "32", "22", "12", "30", "36", "-32", "4", "-35", "42", "17", "-8", "26", "-20", "-37", "-2", "36", "-14", "-38", "3", "-41", "46", "26", "-2", "26" ]
[ "sign" ]
10
1
2
[ "A003961", "A008683", "A323893", "A336840", "A349915", "A378520" ]
null
Antti Karttunen, Nov 30 2024
2025-03-31T01:47:40
oeisdata/seq/A378/A378520.seq
c49d673bc11ee996d446ee9d6cfdcf83
A378521
Möbius transform of A048673.
[ "1", "1", "2", "3", "3", "4", "5", "9", "10", "6", "6", "12", "8", "10", "12", "27", "9", "20", "11", "18", "20", "12", "14", "36", "21", "16", "50", "30", "15", "24", "18", "81", "24", "18", "30", "60", "20", "22", "32", "54", "21", "40", "23", "36", "60", "28", "26", "108", "55", "42", "36", "48", "29", "100", "36", "90", "44", "30", "30", "72", "33", "36", "100", "243", "48", "48", "35", "54", "56", "60", "36", "180", "39", "40", "84", "66", "60", "64", "41", "162", "250" ]
[ "nonn" ]
8
1
3
[ "A000010", "A003961", "A003972", "A008683", "A048673", "A055034", "A072451", "A349136", "A378521" ]
null
Antti Karttunen, Nov 30 2024
2024-11-30T23:47:01
oeisdata/seq/A378/A378521.seq
b8df0ebfd1ed6c94a585db2461b67254
A378522
Lexicographically earliest infinite sequence such that a(i) = a(j) => A378518(i) = A378518(j), for all i, j >= 1.
[ "1", "1", "1", "2", "1", "1", "1", "3", "4", "1", "1", "5", "1", "1", "1", "6", "1", "7", "1", "8", "1", "1", "1", "9", "10", "1", "11", "5", "1", "1", "1", "12", "1", "1", "1", "13", "1", "1", "1", "14", "1", "1", "1", "6", "15", "1", "1", "16", "15", "17", "1", "18", "1", "19", "1", "9", "1", "1", "1", "20", "1", "1", "21", "22", "1", "1", "1", "23", "1", "1", "1", "24", "1", "1", "25", "26", "1", "1", "1", "27", "28", "1", "1", "22", "1", "1", "1", "12", "1", "29", "1", "30", "1", "1", "1", "31", "1", "29", "32", "33", "1", "1", "1", "34", "1" ]
[ "nonn" ]
6
1
4
[ "A005117", "A097248", "A378518", "A378522" ]
null
Antti Karttunen, Nov 30 2024
2024-11-30T16:45:49
oeisdata/seq/A378/A378522.seq
3d9bb9577d26c8ab663b9da1b232f077
A378523
Dirichlet inverse of A332993, where A332993 is defined as a(1) = 1, and for n > 1, a(n) = n + a(A032742(n)), and A032742 is the largest proper divisor.
[ "1", "-3", "-4", "2", "-6", "14", "-8", "0", "3", "20", "-12", "-14", "-14", "26", "27", "0", "-18", "-17", "-20", "-18", "35", "38", "-24", "4", "5", "44", "0", "-22", "-30", "-109", "-32", "0", "51", "56", "53", "34", "-38", "62", "59", "4", "-42", "-137", "-44", "-30", "-30", "74", "-48", "0", "7", "-27", "75", "-34", "-54", "6", "77", "4", "83", "92", "-60", "146", "-62", "98", "-36", "0", "89", "-193", "-68", "-42", "99", "-199", "-72", "-28", "-74", "116" ]
[ "sign" ]
7
1
2
[ "A032742", "A332993", "A378523", "A378524" ]
null
Antti Karttunen, Nov 30 2024
2024-11-30T23:46:44
oeisdata/seq/A378/A378523.seq
8fb60f8f2501922ea98a13b96f861889
A378524
Dirichlet inverse of A333794.
[ "1", "-3", "-6", "2", "-12", "23", "-20", "0", "14", "47", "-36", "-27", "-40", "79", "102", "0", "-48", "-81", "-64", "-57", "174", "143", "-96", "10", "68", "159", "-24", "-97", "-112", "-517", "-116", "0", "314", "191", "360", "170", "-128", "255", "350", "22", "-144", "-885", "-176", "-177", "-400", "383", "-240", "0", "218", "-393", "414", "-197", "-216", "211", "656", "38", "566", "447", "-284", "947", "-232", "463", "-696", "0", "724" ]
[ "sign" ]
6
1
2
[ "A052126", "A333794", "A378523", "A378524" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:18
oeisdata/seq/A378/A378524.seq
241a3cb19dd8067ddaf55a951a21c20f
A378525
Dirichlet inverse of A378542, where A378542 is the sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).
[ "1", "-2", "-3", "-1", "-5", "5", "-7", "2", "-1", "9", "-11", "5", "-13", "13", "14", "0", "-17", "5", "-19", "7", "20", "21", "-23", "-5", "-1", "25", "3", "9", "-29", "-20", "-31", "0", "32", "33", "34", "-4", "-37", "37", "38", "-9", "-41", "-30", "-43", "13", "8", "45", "-47", "-2", "-1", "7", "50", "15", "-53", "-5", "54", "-13", "56", "57", "-59", "-28", "-61", "61", "10", "0", "64", "-50", "-67", "19", "68", "-56", "-71", "-7", "-73", "73", "8", "21", "76" ]
[ "sign" ]
7
1
2
[ "A378525", "A378526", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:27
oeisdata/seq/A378/A378525.seq
8791e80a1ee8fb333b187adbcefe0a8e
A378526
Dirichlet inverse of A378548, where A378548 is the sum of divisors d of n such that n/d is odd with an even number of prime factors (counted with multiplicity).
[ "1", "-2", "-3", "0", "-5", "6", "-7", "0", "-1", "10", "-11", "0", "-13", "14", "14", "0", "-17", "2", "-19", "0", "20", "22", "-23", "0", "-1", "26", "3", "0", "-29", "-28", "-31", "0", "32", "34", "34", "0", "-37", "38", "38", "0", "-41", "-40", "-43", "0", "8", "46", "-47", "0", "-1", "2", "50", "0", "-53", "-6", "54", "0", "56", "58", "-59", "0", "-61", "62", "10", "0", "64", "-64", "-67", "0", "68", "-68", "-71", "0", "-73", "74", "8", "0", "76", "-76", "-79", "0", "0", "82" ]
[ "sign" ]
9
1
2
[ "A023900", "A055615", "A353557", "A358777", "A369454", "A378525", "A378526", "A378527", "A378548" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:00
oeisdata/seq/A378/A378526.seq
c5164b8ecd23c33d4636f07a1190d9af
A378527
Dirichlet inverse of A378546.
[ "1", "-2", "-3", "0", "-5", "6", "-7", "0", "-1", "10", "-11", "-1", "-13", "14", "14", "-1", "-17", "2", "-19", "-1", "20", "22", "-23", "2", "-1", "26", "3", "-1", "-29", "-28", "-31", "2", "32", "34", "34", "3", "-37", "38", "38", "2", "-41", "-40", "-43", "-1", "8", "46", "-47", "3", "-1", "2", "50", "-1", "-53", "-6", "54", "2", "56", "58", "-59", "8", "-61", "62", "10", "0", "64", "-64", "-67", "-1", "68", "-68", "-71", "-6", "-73", "74", "8", "-1", "76", "-76", "-79", "5" ]
[ "sign" ]
8
1
2
[ "A023900", "A055615", "A369974", "A378525", "A378526", "A378527", "A378528", "A378546" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:40:44
oeisdata/seq/A378/A378527.seq
fd8dbfbf5c309b262bd591b9bce637ea
A378528
Dirichlet inverse of A378444.
[ "1", "-1", "-1", "0", "-1", "1", "-1", "0", "-1", "1", "-1", "-1", "-1", "1", "0", "-1", "-1", "1", "-1", "-1", "0", "1", "-1", "1", "-1", "1", "1", "-1", "-1", "0", "-1", "1", "0", "1", "0", "1", "-1", "1", "0", "1", "-1", "0", "-1", "-1", "2", "1", "-1", "1", "-1", "1", "0", "-1", "-1", "-1", "0", "1", "0", "1", "-1", "2", "-1", "1", "2", "0", "0", "0", "-1", "-1", "0", "0", "-1", "-1", "-1", "1", "2", "-1", "0", "0", "-1", "1", "0", "1", "-1", "2", "0", "1", "0", "1", "-1", "-2", "0", "-1", "0", "1", "0", "-1", "-1", "1", "2", "1", "-1", "0", "-1", "1", "2" ]
[ "sign" ]
8
1
45
[ "A000010", "A008683", "A369974", "A378444", "A378527", "A378528" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:05
oeisdata/seq/A378/A378528.seq
bb4626715bc77b84c155583bb6ba65f1
A378529
Characteristic function of A378530.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
8
1
null
[ "A033630", "A064771", "A083206", "A083209", "A378448", "A378449", "A378529", "A378530", "A378604" ]
null
Antti Karttunen, Dec 01 2024
2024-12-02T10:11:16
oeisdata/seq/A378/A378529.seq
0afcefacdd649eb07cf5d94367bf091a
A378530
Numbers which can be written in precisely one way as sum of a subset of their proper divisors and that have exactly one subset of their divisors such that the complement has the same sum.
[ "6", "20", "28", "88", "104", "272", "304", "368", "464", "496", "650", "1184", "1312", "1376", "1504", "1696", "1888", "1952", "3770", "4288", "4544", "4672", "5056", "5312", "5696", "6208", "6464", "6592", "6808", "6848", "6976", "7144", "7232", "8056", "8128", "8925", "10744", "11096", "13192", "13736", "14008", "14552", "14824", "15368", "16768", "17536", "17792", "17816", "19072", "19328", "20096", "20864", "21376", "22144" ]
[ "nonn" ]
8
1
1
[ "A000396", "A064771", "A083209", "A378529", "A378530", "A378604" ]
null
Antti Karttunen, Dec 01 2024
2024-12-02T10:10:47
oeisdata/seq/A378/A378530.seq
34211f66301704ea870643adee9a72af
A378531
Dirichlet convolution of A378432 and A378542.
[ "1", "0", "0", "2", "0", "3", "0", "2", "2", "3", "0", "4", "0", "3", "3", "6", "0", "4", "0", "4", "3", "3", "0", "14", "2", "3", "2", "4", "0", "6", "0", "10", "3", "3", "3", "18", "0", "3", "3", "14", "0", "6", "0", "4", "4", "3", "0", "30", "2", "4", "3", "4", "0", "14", "3", "14", "3", "3", "0", "30", "0", "3", "4", "22", "3", "6", "0", "4", "3", "6", "0", "48", "0", "3", "4", "4", "3", "6", "0", "30", "6", "3", "0", "30", "3", "3", "3", "14", "0", "30", "3", "4", "3", "3", "3", "74", "0", "4", "4", "18" ]
[ "nonn" ]
8
1
4
[ "A008683", "A345182", "A378432", "A378531", "A378532", "A378533", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:43
oeisdata/seq/A378/A378531.seq
8e3444328f443c26fa8735d0ff741fa1
A378532
Dirichlet convolution of A296075 and A378525.
[ "1", "0", "0", "-2", "0", "-3", "0", "-2", "-2", "-3", "0", "-4", "0", "-3", "-3", "-2", "0", "-4", "0", "-4", "-3", "-3", "0", "-2", "-2", "-3", "-2", "-4", "0", "-6", "0", "-2", "-3", "-3", "-3", "-1", "0", "-3", "-3", "-2", "0", "-6", "0", "-4", "-4", "-3", "0", "-2", "-2", "-4", "-3", "-4", "0", "-2", "-3", "-2", "-3", "-3", "0", "0", "0", "-3", "-4", "-2", "-3", "-6", "0", "-4", "-3", "-6", "0", "0", "0", "-3", "-4", "-4", "-3", "-6", "0", "-2", "-2", "-3", "0", "0", "-3", "-3", "-3", "-2" ]
[ "sign" ]
8
1
4
[ "A033879", "A296075", "A378218", "A378525", "A378531", "A378532", "A378534", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:11
oeisdata/seq/A378/A378532.seq
39873309e4a2b051e85804bd73022aa2
A378533
Dirichlet convolution of A323910 and A378542.
[ "1", "1", "1", "3", "1", "4", "1", "5", "3", "4", "1", "10", "1", "4", "4", "11", "1", "10", "1", "10", "4", "4", "1", "26", "3", "4", "5", "10", "1", "16", "1", "21", "4", "4", "4", "34", "1", "4", "4", "26", "1", "16", "1", "10", "10", "4", "1", "62", "3", "10", "4", "10", "1", "26", "4", "26", "4", "4", "1", "56", "1", "4", "10", "43", "4", "16", "1", "10", "4", "16", "1", "98", "1", "4", "10", "10", "4", "16", "1", "62", "11", "4", "1", "56", "4", "4", "4", "26", "1", "56", "4", "10", "4", "4", "4" ]
[ "nonn" ]
9
1
4
[ "A323910", "A378223", "A378531", "A378533", "A378534", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:16
oeisdata/seq/A378/A378533.seq
e1b750f8de4317261b67a721f1d47f79
A378534
Dirichlet convolution of A033879 and A378525.
[ "1", "-1", "-1", "-2", "-1", "-2", "-1", "0", "-2", "-2", "-1", "1", "-1", "-2", "-2", "0", "-1", "1", "-1", "1", "-2", "-2", "-1", "2", "-2", "-2", "0", "1", "-1", "2", "-1", "0", "-2", "-2", "-2", "4", "-1", "-2", "-2", "2", "-1", "2", "-1", "1", "1", "-2", "-1", "0", "-2", "1", "-2", "1", "-1", "2", "-2", "2", "-2", "-2", "-1", "6", "-1", "-2", "1", "0", "-2", "2", "-1", "1", "-2", "2", "-1", "-1", "-1", "-2", "1", "1", "-2", "2", "-1", "0", "0", "-2", "-1", "6", "-2", "-2", "-2", "2", "-1", "6" ]
[ "sign" ]
9
1
4
[ "A008683", "A033879", "A323910", "A378224", "A378532", "A378533", "A378534", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T13:41:21
oeisdata/seq/A378/A378534.seq
cc2fe9b19f99ef4abf3746d124757bb3
A378535
Möbius transform of A378542, where A378542 is the sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).
[ "1", "1", "2", "3", "4", "3", "6", "5", "7", "5", "10", "7", "12", "7", "9", "11", "16", "9", "18", "13", "13", "11", "22", "13", "21", "13", "20", "19", "28", "15", "30", "21", "21", "17", "25", "23", "36", "19", "25", "23", "40", "21", "42", "31", "30", "23", "46", "27", "43", "25", "33", "37", "52", "27", "41", "33", "37", "29", "58", "33", "60", "31", "44", "43", "49", "33", "66", "49", "45", "35", "70", "41", "72", "37", "46", "55", "61", "39", "78", "49", "61", "41", "82" ]
[ "nonn" ]
7
1
3
[ "A001222", "A008683", "A378535", "A378536" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T19:54:25
oeisdata/seq/A378/A378535.seq
2ead33a230e1ecbaa644e77f584e3aad
A378536
Inverse Möbius transform of A378525.
[ "1", "-1", "-2", "-2", "-4", "1", "-6", "0", "-3", "3", "-10", "5", "-12", "5", "7", "0", "-16", "5", "-18", "9", "11", "9", "-22", "2", "-5", "11", "0", "13", "-28", "-1", "-30", "0", "19", "15", "23", "5", "-36", "17", "23", "2", "-40", "-3", "-42", "21", "14", "21", "-46", "0", "-7", "9", "31", "25", "-52", "3", "39", "2", "35", "27", "-58", "-18", "-60", "29", "20", "0", "47", "-7", "-66", "33", "43", "-13", "-70", "-5", "-72", "35", "14", "37", "59", "-9", "-78", "0", "0" ]
[ "sign" ]
8
1
3
[ "A378525", "A378535", "A378536", "A378542" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T19:54:30
oeisdata/seq/A378/A378536.seq
4ccda50037a270d27a8e8809823c1b17
A378537
Characteristic function for primitive Zumkeller numbers.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
13
1
null
[ "A083206", "A179527", "A180332", "A341619", "A378446", "A378454", "A378537", "A378538", "A378539" ]
null
Antti Karttunen, Dec 02 2024
2024-12-05T13:51:52
oeisdata/seq/A378/A378537.seq
56f3a3ddeaa9e6b56cabf86ca089f707
A378538
Symmetric difference of the primitive non-deficient numbers and the primitive Zumkeller numbers.
[ "748", "7544", "8228", "10184", "12716", "17204", "21692", "23188", "27676", "30668", "32164", "35156", "39644", "44132", "45628", "50116", "53108", "54604", "56816", "59092", "61904", "62084", "62416", "66572", "66928", "69488", "72556", "73616", "75548", "77044", "80036", "81532", "84524", "94996", "97988", "102416", "102476", "103972", "111452", "112948", "117436", "121924", "124916", "129404" ]
[ "nonn" ]
13
1
1
[ "A006039", "A180332", "A341619", "A378537", "A378538", "A378656", "A378657" ]
null
Antti Karttunen, Dec 02 2024
2024-12-05T13:51:45
oeisdata/seq/A378/A378538.seq
cac20fab2c3cb95099e2fb4352d7a87f
A378539
Characteristic function for numbers that have Zumkeller divisors.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
12
1
null
[ "A083206", "A294936", "A376880", "A378446", "A378537", "A378538", "A378539" ]
null
Antti Karttunen, Dec 02 2024
2024-12-02T16:02:11
oeisdata/seq/A378/A378539.seq
e04b38806c9780264a04396b392cf3a3
A378540
a(n) = 1 if n is a practical number (A005153) that is neither a square or twice a square, otherwise a(n) = 0.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
11
1
null
[ "A000203", "A005153", "A053866", "A179527", "A322860", "A353061", "A378540", "A378541" ]
null
Antti Karttunen, Dec 02 2024
2024-12-02T09:50:10
oeisdata/seq/A378/A378540.seq
fa5447e8c1c4b93e55592941f2d7b77c
A378541
Practical numbers whose sum of divisors is even.
[ "6", "12", "20", "24", "28", "30", "40", "42", "48", "54", "56", "60", "66", "78", "80", "84", "88", "90", "96", "104", "108", "112", "120", "126", "132", "140", "150", "156", "160", "168", "176", "180", "192", "198", "204", "208", "210", "216", "220", "224", "228", "234", "240", "252", "260", "264", "270", "272", "276", "280", "294", "300", "304", "306", "308", "312", "320", "330", "336", "340", "342", "348", "352", "360", "364", "368", "378", "380" ]
[ "nonn" ]
11
1
1
[ "A005153", "A028983", "A083207", "A353061", "A378540", "A378541" ]
null
Antti Karttunen and David A. Corneth, Dec 02 2024
2024-12-03T11:46:01
oeisdata/seq/A378/A378541.seq
0ffc3e60965de03e4201e0dea461650e
A378542
Sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).
[ "1", "2", "3", "5", "5", "7", "7", "10", "10", "11", "11", "17", "13", "15", "16", "21", "17", "23", "19", "27", "22", "23", "23", "35", "26", "27", "30", "37", "29", "40", "31", "42", "34", "35", "36", "56", "37", "39", "40", "55", "41", "54", "43", "57", "53", "47", "47", "73", "50", "57", "52", "67", "53", "70", "56", "75", "58", "59", "59", "96", "61", "63", "73", "85", "66", "82", "67", "87", "70", "84", "71", "115", "73", "75", "83", "97", "78", "96", "79", "115", "91" ]
[ "nonn" ]
11
1
2
[ "A000010", "A000027", "A000203", "A001222", "A038548", "A065043", "A378525", "A378542", "A378543", "A378546", "A378548" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:02
oeisdata/seq/A378/A378542.seq
37e1fcc8ae2a1425fa8ec28be3f94229
A378543
Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).
[ "0", "1", "1", "2", "1", "5", "1", "5", "3", "7", "1", "11", "1", "9", "8", "10", "1", "16", "1", "15", "10", "13", "1", "25", "5", "15", "10", "19", "1", "32", "1", "21", "14", "19", "12", "35", "1", "21", "16", "35", "1", "42", "1", "27", "25", "25", "1", "51", "7", "36", "20", "31", "1", "50", "16", "45", "22", "31", "1", "72", "1", "33", "31", "42", "18", "62", "1", "39", "26", "60", "1", "80", "1", "39", "41", "43", "18", "72", "1", "71", "30", "43", "1", "94", "22", "45", "32", "65" ]
[ "nonn" ]
11
1
4
[ "A000010", "A000027", "A000203", "A056924", "A066829", "A378542", "A378543", "A378547", "A378549" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:06
oeisdata/seq/A378/A378543.seq
1e768017be898fa4eff9767407791114
A378544
a(n) is the sum of those divisors d of n for which A083345(d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "1", "1", "1", "1", "1", "1", "1", "1", "10", "1", "1", "13", "1", "1", "16", "17", "1", "10", "1", "21", "22", "1", "1", "13", "26", "1", "10", "29", "1", "16", "1", "17", "34", "1", "36", "22", "1", "1", "40", "21", "1", "22", "1", "45", "25", "1", "1", "29", "50", "26", "52", "53", "1", "10", "56", "29", "58", "1", "1", "48", "1", "1", "31", "17", "66", "34", "1", "69", "70", "36", "1", "22", "1", "1", "41", "77", "78", "40", "1", "37", "91", "1", "1", "62", "86", "1", "88", "45", "1", "25" ]
[ "nonn" ]
6
1
9
[ "A000203", "A369001", "A378444", "A378544", "A378545" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T21:04:36
oeisdata/seq/A378/A378544.seq
dd42519d96d8ab8a722da6d4dc60f2de
A378545
a(n) is the sum of those divisors d of n for which A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "0", "2", "3", "6", "5", "11", "7", "14", "3", "17", "11", "15", "13", "23", "8", "14", "17", "29", "19", "21", "10", "35", "23", "47", "5", "41", "30", "27", "29", "56", "31", "46", "14", "53", "12", "69", "37", "59", "16", "69", "41", "74", "43", "39", "53", "71", "47", "95", "7", "67", "20", "45", "53", "110", "16", "91", "22", "89", "59", "120", "61", "95", "73", "110", "18", "110", "67", "57", "26", "108", "71", "173", "73", "113", "83", "63", "18", "128", "79", "149" ]
[ "nonn" ]
7
1
2
[ "A000203", "A377874", "A378445", "A378544", "A378545" ]
null
Antti Karttunen, Nov 29 2024
2024-11-29T21:04:41
oeisdata/seq/A378/A378545.seq
2fcd4e654451f91bc2bc5550e0386f1e
A378546
a(n) is the sum of the divisors d of n for which A083345(n/d) is even, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "1", "2", "3", "4", "5", "6", "7", "8", "10", "10", "11", "13", "13", "14", "16", "17", "17", "20", "19", "21", "22", "22", "23", "26", "26", "26", "30", "29", "29", "32", "31", "34", "34", "34", "36", "43", "37", "38", "40", "42", "41", "44", "43", "45", "53", "46", "47", "55", "50", "52", "52", "53", "53", "60", "56", "58", "58", "58", "59", "72", "61", "62", "73", "68", "66", "68", "67", "69", "70", "72", "71", "86", "73", "74", "83", "77", "78", "80", "79", "89", "91" ]
[ "nonn" ]
7
1
2
[ "A000010", "A000027", "A000203", "A083345", "A369001", "A378444", "A378544", "A378545", "A378546", "A378547" ]
null
Antti Karttunen, Nov 30 2024
2024-11-30T08:50:15
oeisdata/seq/A378/A378546.seq
c5ff52ad000309f27396eb02db36e5b2
A378547
a(n) is the sum of the divisors d of n for which A083345(n/d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
[ "0", "1", "1", "3", "1", "6", "1", "7", "3", "8", "1", "15", "1", "10", "8", "14", "1", "19", "1", "21", "10", "14", "1", "34", "5", "16", "10", "27", "1", "40", "1", "29", "14", "20", "12", "48", "1", "22", "16", "48", "1", "52", "1", "39", "25", "26", "1", "69", "7", "41", "20", "45", "1", "60", "16", "62", "22", "32", "1", "96", "1", "34", "31", "59", "18", "76", "1", "57", "26", "72", "1", "109", "1", "40", "41", "63", "18", "88", "1", "97", "30", "44", "1", "126", "22", "46", "32" ]
[ "nonn" ]
9
1
4
[ "A000010", "A000027", "A000203", "A083345", "A377874", "A378445", "A378544", "A378545", "A378546", "A378547" ]
null
Antti Karttunen, Nov 30 2024
2024-11-30T08:50:18
oeisdata/seq/A378/A378547.seq
8256ff7695e523dd9bfdc9a2c48c07b5
A378548
Sum of divisors d of n such that n/d is odd with an even number of prime factors (counted with multiplicity).
[ "1", "2", "3", "4", "5", "6", "7", "8", "10", "10", "11", "12", "13", "14", "16", "16", "17", "20", "19", "20", "22", "22", "23", "24", "26", "26", "30", "28", "29", "32", "31", "32", "34", "34", "36", "40", "37", "38", "40", "40", "41", "44", "43", "44", "53", "46", "47", "48", "50", "52", "52", "52", "53", "60", "56", "56", "58", "58", "59", "64", "61", "62", "73", "64", "66", "68", "67", "68", "70", "72", "71", "80", "73", "74", "83", "76", "78", "80", "79", "80", "91", "82" ]
[ "nonn" ]
13
1
2
[ "A000010", "A000203", "A002131", "A353557", "A369257", "A378526", "A378542", "A378546", "A378548", "A378549" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:10
oeisdata/seq/A378/A378548.seq
f15f5e5911fe1fe645388af772b5e9f8
A378549
Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).
[ "0", "1", "1", "3", "1", "6", "1", "7", "3", "8", "1", "16", "1", "10", "8", "15", "1", "19", "1", "22", "10", "14", "1", "36", "5", "16", "10", "28", "1", "40", "1", "31", "14", "20", "12", "51", "1", "22", "16", "50", "1", "52", "1", "40", "25", "26", "1", "76", "7", "41", "20", "46", "1", "60", "16", "64", "22", "32", "1", "104", "1", "34", "31", "63", "18", "76", "1", "58", "26", "72", "1", "115", "1", "40", "41", "64", "18", "88", "1", "106", "30", "44", "1", "136", "22", "46", "32" ]
[ "nonn" ]
9
1
4
[ "A000203", "A353557", "A378543", "A378547", "A378548", "A378549" ]
null
Antti Karttunen, Dec 01 2024
2024-12-01T10:05:14
oeisdata/seq/A378/A378549.seq
a7ce9b235d226b6cc6a3a4bcacdad250
A378550
a(n) = 1 if sigma(n) >= 2*n-1, otherwise 0.
[ "1", "1", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1" ]
[ "nonn" ]
16
1
null
[ "A000203", "A103288", "A120444", "A209229", "A294936", "A378550" ]
null
Antti Karttunen, Dec 01 2024
2024-12-02T11:03:39
oeisdata/seq/A378/A378550.seq
2db532a53d26126d11107590d1d80c16
A378551
a(n) = Sum_{k=0..n} 4^k * binomial(n/2+k-1,k) * binomial(n-1,n-k).
[ "1", "2", "20", "206", "2200", "24062", "267500", "3009050", "34150000", "390265190", "4484762500", "51771831146", "599921125000", "6974108163778", "81297715937500", "949957147566086", "11123368187500000", "130487420114543110", "1533247106445312500", "18042303960492212810", "212590835968046875000" ]
[ "nonn" ]
13
0
2
[ "A002002", "A372109", "A378551", "A378552" ]
null
Seiichi Manyama, Nov 30 2024
2024-11-30T09:49:24
oeisdata/seq/A378/A378551.seq
e427c168e539ffd481de85ee6c7d7ed4
A378552
a(n) = Sum_{k=0..n} 9^k * binomial(n/3+k-1,k) * binomial(n-1,n-k).
[ "1", "3", "51", "900", "16455", "307833", "5850000", "112445112", "2180050215", "42552000000", "835075676361", "16461248223588", "325696500000000", "6464447754891285", "128654307202482420", "2566472490000000000", "51302899404879842343", "1027391467409893403745", "20607804108000000000000" ]
[ "nonn" ]
14
0
2
[ "A002002", "A372110", "A378551", "A378552" ]
null
Seiichi Manyama, Nov 30 2024
2024-11-30T09:49:39
oeisdata/seq/A378/A378552.seq
397e435e2c18307513820f314fefeea8
A378553
The number of n-digit composite numbers with all digits distinct.
[ "4", "61", "551", "4026", "24687", "125841", "510370", "1542450", "3120693", "3265920" ]
[ "nonn", "base", "fini", "full" ]
21
1
1
[ "A073531", "A073532", "A210441", "A378553" ]
null
Shyam Sunder Gupta, Nov 30 2024
2024-12-01T10:06:22
oeisdata/seq/A378/A378553.seq
357c10ee3eb451dea0d0a8d769dd409a
A378554
a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k-1,k) * binomial(k/2,n-k).
[ "1", "1", "7", "28", "171", "846", "4942", "26580", "153363", "856900", "4939682", "28140476", "162676878", "936947116", "5436375532", "31526252208", "183571246659", "1069552636950", "6247183319938", "36524006501180", "213899020967786", "1253905101529080", "7359775341696180", "43237184121401400" ]
[ "nonn" ]
14
0
3
[ "A213684", "A372125", "A378554", "A378555" ]
null
Seiichi Manyama, Nov 30 2024
2024-11-30T09:49:54
oeisdata/seq/A378/A378554.seq
63a82809a87ccd989fc36dc44fd2e8c1
A378555
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k-1,k) * binomial(k/3,n-k).
[ "1", "1", "9", "19", "305", "156", "13233", "-23988", "688113", "-2863070", "41085704", "-246536784", "2696513885", "-19410931916", "187672944300", "-1481383572516", "13522625165601", "-111877103550195", "994511499413664", "-8430550720540365", "74061353032540020", "-636000265949289978" ]
[ "sign" ]
13
0
3
[ "A213684", "A372126", "A378554", "A378555" ]
null
Seiichi Manyama, Nov 30 2024
2024-11-30T09:50:09
oeisdata/seq/A378/A378555.seq
909088bf2eeb1d83fbc744ef1c2c8d9d
A378556
Powers of 2 that do not include the digit 2.
[ "1", "4", "8", "16", "64", "4096", "16384", "65536", "1048576", "4194304", "8388608", "67108864", "17179869184", "34359738368", "68719476736", "549755813888", "4398046511104", "70368744177664", "18014398509481984", "18446744073709551616", "18889465931478580854784", "9671406556917033397649408", "374144419156711147060143317175368453031918731001856" ]
[ "nonn", "base" ]
10
1
2
[ "A000079", "A034293", "A378556" ]
null
Erich Friedman, Nov 30 2024
2024-12-12T23:32:03
oeisdata/seq/A378/A378556.seq
60904f484f3e7b3c62955230093e12f4
A378557
Powers of 3 that do not contain the digit 3.
[ "1", "9", "27", "81", "729", "2187", "6561", "59049", "177147", "4782969", "1162261467", "7625597484987", "22876792454961", "16677181699666569", "12157665459056928801", "717897987691852588770249", "174449211009120179071170507", "11972515182562019788602740026717047105681" ]
[ "nonn", "base", "fini" ]
8
1
2
[ "A000244", "A131629", "A378557" ]
null
Erich Friedman, Nov 30 2024
2024-12-12T23:32:27
oeisdata/seq/A378/A378557.seq
4ffc476e4f9170e35c6cefc43927d9d9
A378558
Powers of 4 that do not include the digit 4.
[ "1", "16", "256", "65536", "16777216", "1099511627776" ]
[ "nonn", "base", "hard", "more" ]
4
1
2
[ "A000302", "A378558" ]
null
Erich Friedman, Nov 30 2024
2024-12-04T11:44:05
oeisdata/seq/A378/A378558.seq
3ff989a7e01888db1c50b2592b324a8d
A378559
a(n) = t is the smallest prime t > p = prime(n) for which t == p (mod k) for all k = 2,...,p-1.
[ "3", "5", "17", "67", "2531", "27733", "2162177", "12252259", "465585143", "240940299629", "6987268688431", "577614211574437", "48086383113568841", "438120379479182443", "75356705270419372847", "27891400538213970357653", "5584478196651286064932859", "38762848659108926803651261", "23645337682056445350227232067" ]
[ "nonn" ]
24
1
1
[ "A000040", "A058254", "A378559" ]
null
Tamas Sandor Nagy, Nov 30 2024
2024-12-13T21:56:18
oeisdata/seq/A378/A378559.seq
2526a8d66c1eb22f1584d0eb2f58fa92
A378560
Numbers with the median of the digits equal to one of the digits.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "22", "33", "44", "55", "66", "77", "88", "99", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124", "125", "126", "127", "128", "129", "130", "131", "132", "133", "134", "135", "136", "137", "138", "139", "140" ]
[ "nonn", "base", "easy" ]
17
1
3
[ "A001633", "A175688", "A292730", "A292739", "A366207", "A366208", "A366209", "A366210", "A366211", "A366212", "A366213", "A366214", "A378560", "A378564" ]
null
Stefano Spezia, Nov 30 2024
2024-12-03T11:45:08
oeisdata/seq/A378/A378560.seq
7171361c4022225dd6b2eaf7419e1f91
A378561
Number of ways to place k nonattacking anassas on an n X n chess board. Triangle T(n,k) read by rows.
[ "1", "1", "1", "1", "4", "3", "1", "9", "22", "14", "1", "16", "82", "156", "90", "1", "25", "220", "840", "1366", "738", "1", "36", "485", "3100", "9796", "14288", "7364", "1", "49", "938", "9030", "46816", "129360", "174112", "86608", "1", "64", "1652", "22344", "172116", "767424", "1916776", "2424880", "1173240", "1", "81", "2712", "49056", "525756", "3442740", "13682320", "31572720", "38019496", "17990600" ]
[ "nonn", "easy", "tabl" ]
35
0
5
[ "A000012", "A000290", "A088789", "A378561" ]
null
Eder G. Santos, Nov 30 2024
2024-12-28T10:19:49
oeisdata/seq/A378/A378561.seq
85d3087266a0e6678d526ca31de3c27f
A378562
a(n) is the number of steps to reach 1 by reversing digits of n in the lowest base where reversal reduces the number.
[ "0", "1", "1", "1", "1", "2", "2", "1", "1", "2", "3", "2", "4", "3", "3", "1", "5", "2", "4", "2", "2", "5", "5", "2", "5", "4", "1", "3", "6", "4", "4", "1", "5", "6", "4", "2", "5", "6", "5", "2", "6", "3", "5", "5", "3", "7", "7", "2", "5", "5", "6", "4", "6", "2", "7", "3", "6", "6", "8", "4", "8", "5", "2", "1", "9", "6", "7", "6", "6", "6", "8", "2", "5", "7", "6", "6", "9", "7", "7", "2", "7", "6", "7", "3", "5", "7", "8" ]
[ "nonn", "base", "easy" ]
32
1
6
[ "A004086", "A030101", "A378562" ]
null
Asier Rodriguez Escalante, Nov 30 2024
2024-12-16T14:58:56
oeisdata/seq/A378/A378562.seq
44b4948c5965f99f1fca9f253a7e194c
A378563
Primes that remain prime if any three of their digits are deleted.
[ "2237", "2273", "2333", "2357", "2377", "2557", "2753", "2777", "3253", "3257", "3323", "3373", "3527", "3533", "3557", "3727", "3733", "5227", "5233", "5237", "5273", "5323", "5333", "5527", "5557", "5573", "5737", "7237", "7253", "7333", "7523", "7537", "7573", "7577", "7723", "7727", "7753", "7757", "11113", "11117", "11119", "11131", "11171", "11173", "11197" ]
[ "nonn", "base", "less" ]
21
1
1
[ "A019546", "A051362", "A378081", "A378563" ]
null
Enrique Navarrete, Nov 30 2024
2024-12-03T12:49:39
oeisdata/seq/A378/A378563.seq
496e9e7ee615cdeee55f3cb39d19dff9
A378564
a(n) is the number of n-digit nonnegative integers with the median of the digits equal to one of the digits.
[ "10", "9", "900", "1665", "90000", "232710", "9000000", "29055165", "900000000", "3413319138", "90000000000", "386095933170", "9000000000000", "42568084276236", "900000000000000", "4607838122919165", "90000000000000000", "491998811785538730", "9000000000000000000", "51983526276872387430", "900000000000000000000", "5447302810160797285236" ]
[ "nonn", "base" ]
28
1
1
[ "A063945", "A179239", "A378560", "A378564" ]
null
Stefano Spezia, Dec 01 2024
2024-12-16T02:07:33
oeisdata/seq/A378/A378564.seq
7b542da49b615d65ad6151953e19927e
A378565
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+k-1,n-k).
[ "1", "1", "7", "43", "271", "1746", "11425", "75615", "504799", "3392953", "22930282", "155664356", "1060710457", "7250779238", "49700101101", "341474150583", "2351032782783", "16216401440106", "112035931072915", "775163096510445", "5370301986029066", "37249469056575504", "258648802856972348" ]
[ "nonn" ]
9
0
3
[ "A002002", "A011270", "A362087", "A378565", "A378566", "A378567" ]
null
Seiichi Manyama, Dec 01 2024
2024-12-01T05:24:33
oeisdata/seq/A378/A378565.seq
771b837e7110d38539e51f310a497fa8
A378566
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+2*k-1,n-k).
[ "1", "1", "9", "64", "465", "3456", "26082", "199060", "1532313", "11875015", "92528414", "724187982", "5689127886", "44834549501", "354289977750", "2806262293824", "22273793685609", "177113634045858", "1410633764438967", "11251419724586850", "89860413370562730", "718528004169570925" ]
[ "nonn" ]
9
0
3
[ "A002002", "A052529", "A362088", "A365150", "A378565", "A378566", "A378567" ]
null
Seiichi Manyama, Dec 01 2024
2024-12-01T06:14:58
oeisdata/seq/A378/A378566.seq
bf457ff4603b217527d87c15c4994988
A378567
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+3*k-1,n-k).
[ "1", "1", "11", "88", "715", "5951", "50288", "429696", "3702987", "32125390", "280211701", "2454992618", "21588647392", "190444368401", "1684556756320", "14935618142768", "132695019071499", "1181070210132582", "10529299131757754", "94005323670592130", "840373149466892965", "7521508912742542806" ]
[ "nonn" ]
11
0
3
[ "A002002", "A055991", "A367234", "A378565", "A378566", "A378567" ]
null
Seiichi Manyama, Dec 01 2024
2024-12-01T10:54:42
oeisdata/seq/A378/A378567.seq
be316afd67fc0e61e32ddc423f9e1cc6
A378568
Lowest weight of rational fraction with denominator n.
[ "1", "2", "3", "2", "4", "2", "5", "2", "3", "2", "6", "2", "6", "2", "3", "2", "7", "2", "7", "2", "3", "2", "8", "2", "4", "2", "3", "2", "8", "2", "8", "2", "3", "2", "4", "2", "9", "2", "3", "2", "9", "2", "9", "2", "3", "2", "9", "2", "5", "2", "3", "2", "10", "2", "4", "2", "3", "2", "10", "2", "10", "2", "3", "2", "4", "2", "10", "2", "3", "2", "10", "2", "10", "2", "3", "2", "5", "2", "10", "2", "3", "2", "11", "2" ]
[ "nonn" ]
18
1
2
[ "A178031", "A378568" ]
null
Jeffrey Shallit, Dec 01 2024
2024-12-03T12:24:25
oeisdata/seq/A378/A378568.seq
53d91eae2f7f2c4cf8b6e0591f14a258
A378569
a(n) = 3*n*(n+1) + 7.
[ "7", "13", "25", "43", "67", "97", "133", "175", "223", "277", "337", "403", "475", "553", "637", "727", "823", "925", "1033", "1147", "1267", "1393", "1525", "1663", "1807", "1957", "2113", "2275", "2443", "2617", "2797", "2983", "3175", "3373", "3577", "3787", "4003", "4225", "4453", "4687", "4927", "5173", "5425", "5683", "5947", "6217", "6493", "6775", "7063", "7357", "7657", "7963", "8275", "8593", "8917", "9247", "9583", "9925" ]
[ "nonn", "easy" ]
52
0
1
[ "A001043", "A102724", "A378569" ]
null
M. F. Hasler, Feb 04 2025
2025-02-08T04:56:14
oeisdata/seq/A378/A378569.seq
70054c85188263201f4ec926c2c741aa
A378570
Smallest integer m for which A378568(m) = n.
[ "1", "2", "3", "5", "7", "11", "17", "23", "37", "53", "83", "113", "197", "331", "421", "739", "1087", "1663", "2671", "3847", "5903", "10099", "15061", "24683", "38069", "62099", "96323", "141319", "234863", "367163", "589297", "909691" ]
[ "nonn", "more" ]
16
1
2
[ "A378568", "A378570" ]
null
Jeffrey Shallit, Dec 01 2024
2024-12-09T19:20:17
oeisdata/seq/A378/A378570.seq
43618146e2a559fef9b90be248368dee
A378571
G.f. A(x) satisfies 1/x = Sum_{n=-oo..+oo} A(x)^(2*n) * (A(x)^n + 1)^(2*n+1).
[ "1", "1", "2", "5", "17", "56", "190", "670", "2452", "9139", "34512", "131960", "510376", "1992650", "7840845", "31063216", "123809267", "496117444", "1997461096", "8076398383", "32780982554", "133516673419", "545535083011", "2235451243956", "9184586572401", "37828126885778", "156152936538097", "645942256355057", "2677202474308391" ]
[ "nonn" ]
14
1
3
null
null
Paul D. Hanna, Dec 29 2024
2024-12-30T04:26:33
oeisdata/seq/A378/A378571.seq
215e104c017858a59101f49eab21d9ad
A378572
G.f. A(x) satisfies 1/x = Sum_{n=-oo..+oo} A(x)^(2*n) * (A(x)^n + 2)^(2*n+1).
[ "1", "1", "5", "14", "89", "371", "2161", "10696", "61969", "335434", "1952772", "11086400", "65242174", "381110396", "2268552339", "13498467880", "81190422545", "489403577479", "2970230729380", "18078456241060", "110557602461243", "678051379830676", "4173297748385770", "25753520575460880", "159374541532819470", "988579243982587598" ]
[ "nonn" ]
7
1
3
[ "A378571", "A378572" ]
null
Paul D. Hanna, Dec 30 2024
2024-12-30T17:03:35
oeisdata/seq/A378/A378572.seq
b84b283f496bee3486969fd22a7ed519
A378573
G.f. A(x) = Sum_{n=-oo..+oo} x^n * (1 + x^(3*n+1))^(2*n).
[ "1", "1", "1", "2", "1", "1", "1", "4", "1", "2", "1", "6", "1", "1", "1", "8", "7", "1", "2", "10", "1", "1", "1", "27", "1", "1", "1", "14", "11", "1", "30", "16", "1", "1", "1", "18", "1", "46", "36", "20", "1", "1", "1", "37", "67", "2", "1", "24", "85", "1", "1", "117", "1", "1", "1", "28", "71", "1", "286", "30", "1", "22", "1", "33", "1", "154", "1", "34", "287", "211", "1", "36", "191", "1", "1", "38", "1", "127", "456", "271", "1", "1", "524", "42", "2", "1", "277", "44", "681", "1", "1", "46", "1", "788", "1", "1049" ]
[ "nonn" ]
10
0
4
[ "A260147", "A378573" ]
null
Paul D. Hanna, Dec 10 2024
2024-12-11T09:27:38
oeisdata/seq/A378/A378573.seq
b31e4f499da8e5969f8a830580cc94a5
A378574
G.f. A(x) satisfies 1/x = Sum_{n=-oo..+oo} A(x)^(3*n) * (A(x)^n - 1)^(2*n).
[ "1", "3", "12", "59", "327", "1946", "12134", "78226", "517184", "3487505", "23893646", "165850488", "1163828396", "8242924994", "58847504503", "423033663392", "3059510702675", "22246091978206", "162526826216002", "1192478814606035", "8783088349526872", "64916842264368857", "481332209801339757", "3579243987499087418", "26686563090217529433", "199460739112873554700" ]
[ "nonn" ]
9
1
2
null
null
Paul D. Hanna, Jan 10 2025
2025-01-22T04:22:19
oeisdata/seq/A378/A378574.seq
1004ffe73bb129c2c703844be0075500
A378575
G.f. satisfies A(x) = x + x*A(A(A(A(A(x))))), so that this sequence shifts left under the 5th self-COMPOSE.
[ "1", "1", "5", "45", "545", "7945", "132005", "2423501", "48224129", "1026722489", "23177970949", "551133715197", "13734995332769", "357361170997321", "9677345660994725", "272075021315860781", "7925076713952829697", "238747406787319312025", "7427421640015549840133", "238301672444134819413533", "7875799810817511976148129" ]
[ "nonn" ]
9
1
3
[ "A030266", "A091713", "A196523", "A378575" ]
null
Paul D. Hanna, Dec 01 2024
2024-12-03T08:57:04
oeisdata/seq/A378/A378575.seq
e0b7a3202d98970441adfe8207ab8101
A378576
G.f. satisfies A(x) = x + x*A(A(A(A(A(A(x)))))), so that this sequence shifts left under the 6th self-COMPOSE.
[ "1", "1", "6", "66", "981", "17576", "359101", "8109026", "198480901", "5197916551", "144326504376", "4220683214771", "129349023338616", "4138098976882836", "137770738524681831", "4761510500867829696", "170476220596490911691", "6311806909067054474161", "241301669599996597349506", "9512867537981387958217696", "386276838889195561353811321" ]
[ "nonn" ]
10
1
3
[ "A030266", "A091713", "A196523", "A378575", "A378576" ]
null
Paul D. Hanna, Dec 01 2024
2024-12-03T08:57:00
oeisdata/seq/A378/A378576.seq
61738dff591ea01227958c8deda1c66d
A378577
G.f. A(x) equals the series obtained by removing all factors of 2 from the coefficients in 1 + x*A(x)^2.
[ "1", "1", "1", "3", "1", "9", "13", "55", "5", "201", "309", "1467", "541", "7009", "10905", "53103", "2493", "232713", "369973", "1895875", "711901", "10057761", "15917809", "80998215", "7682147", "389278901", "625035439", "3285433779", "1245382467", "18187624005", "29024837139", "150736553103", "7191395811", "735853765941", "1190542570455", "6387028801323", "2429801651419" ]
[ "nonn" ]
36
0
4
[ "A000108", "A000265", "A378577", "A378578" ]
null
Paul D. Hanna, Dec 31 2024
2025-01-03T13:46:33
oeisdata/seq/A378/A378577.seq
b97120ed1491fbe630be6433afe9df0c
A378578
G.f. A(x) equals the series obtained by removing all factors of 3 from the coefficients in 1 + x*A(x)^3.
[ "1", "1", "1", "2", "13", "19", "52", "412", "73", "1405", "11735", "20000", "7300", "388606", "664316", "2325118", "20832709", "11815463", "95438089", "861817318", "1495813613", "5231996647", "47291366710", "3025568936", "199838851432", "1828302724054", "3320026962314", "439614522008", "73390614310810", "131344935434920", "55179693272894", "3321671735661494" ]
[ "nonn" ]
36
0
4
[ "A001764", "A085358", "A282162", "A378577", "A378578" ]
null
Paul D. Hanna, Jan 03 2025
2025-01-04T07:38:42
oeisdata/seq/A378/A378578.seq
24751d6ff6da75bbcc3cf040765240cf
A378579
G.f. A(x) satisfies x = Sum_{n>=1} ((1 + A(x)^n)^n - 1).
[ "1", "-2", "5", "-15", "54", "-226", "1041", "-5045", "25090", "-126674", "646764", "-3335207", "17359589", "-91138625", "482237135", "-2569446532", "13774698084", "-74245779493", "402105384051", "-2187066640025", "11941274232967", "-65425584835537", "359598131529024", "-1982178299221646", "10955208670488609", "-60696056311093958", "337040131916813474" ]
[ "sign" ]
8
1
2
[ "A318636", "A378579" ]
null
Paul D. Hanna, Jan 08 2025
2025-01-09T08:05:39
oeisdata/seq/A378/A378579.seq
219f97a8d4160f32168bdbcdb845e683
A378580
G.f. A(x) satisfies: A(x/A(x)) = theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2).
[ "1", "2", "4", "16", "98", "756", "6848", "70000", "787056", "9569826", "124370360", "1713226992", "24860431856", "378218126868", "6010370135104", "99468568904400", "1710121704611906", "30480806331592708", "562231440303009620", "10715761300881113920", "210744962672423341936", "4271551132579921199584", "89130266684802577438240", "1912639214122430854041680" ]
[ "nonn" ]
12
0
2
[ "A378580", "A378581" ]
null
Paul D. Hanna, Jan 08 2025
2025-01-08T10:33:24
oeisdata/seq/A378/A378580.seq
382a4e5deaa64c0a6570d7e5d0b149a1
A378581
G.f. A(x) satisfies: A(x*A(x)) = theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2).
[ "1", "2", "-4", "24", "-206", "2188", "-26576", "356256", "-5160752", "79686506", "-1299165768", "22211945640", "-396222547760", "7345603921884", "-141098657566176", "2801320345878432", "-57369641880769342", "1209942879994238244", "-26242709149500081668", "584654250865238224808", "-13365654058060024304848", "313249005854811783089504" ]
[ "sign" ]
8
0
2
[ "A378580", "A378581" ]
null
Paul D. Hanna, Jan 08 2025
2025-01-09T08:05:26
oeisdata/seq/A378/A378581.seq
2f86df44f8d12c9372ecaeb74dba5682
A378582
G.f. Sum_{n=-oo..+oo} (x^n - x)^(n+1).
[ "2", "-1", "1", "-1", "4", "-3", "-1", "-1", "13", "-1", "-7", "-10", "10", "-1", "22", "-1", "10", "-23", "-25", "-1", "43", "-1", "50", "-36", "14", "-1", "-19", "-26", "16", "-55", "78", "-1", "201", "-1", "-129", "-78", "20", "-108", "211", "-1", "22", "-105", "9", "-1", "349", "-1", "274", "-430", "26", "-1", "-421", "-50", "568", "-171", "441", "-1", "769", "-661", "-238", "-210", "32", "-1", "1291", "-1", "34", "-591", "-897", "-1288", "1765", "-1" ]
[ "sign" ]
15
0
1
[ "A290003", "A378582", "A379764" ]
null
Paul D. Hanna, Jan 13 2025
2025-01-13T19:18:20
oeisdata/seq/A378/A378582.seq
60bf7d5a7c0bd1790593612f9c1d16de
A378583
G.f. A(x) satisfies 1 + 3*A(x) = Sum_{n=-oo..+oo} (x + A(x)^n)^n.
[ "1", "1", "2", "5", "18", "55", "187", "659", "2411", "8888", "33416", "127319", "490666", "1907591", "7477478", "29515731", "117220905", "468044260", "1877832933", "7566468733", "30606272800", "124236563076", "505910379074", "2066156255657", "8460839330649", "34732196347032", "142901886406430", "589193519802745", "2434038051129212", "10073675500966903" ]
[ "nonn" ]
12
1
3
[ "A378583", "A378584" ]
null
Paul D. Hanna, Jan 10 2025
2025-01-22T04:11:03
oeisdata/seq/A378/A378583.seq
f6053fd074498a1ae92df7adcdfdbdec
A378584
G.f. A(x) satisfies 1 + 4*A(x) = Sum_{n=-oo..+oo} (2*x + A(x)^n)^n.
[ "1", "2", "5", "13", "46", "170", "666", "2648", "10944", "46296", "199828", "873616", "3863994", "17255100", "77710773", "352486026", "1608824138", "7383210030", "34048297506", "157700809314", "733283992543", "3421740870626", "16018406425836", "75208586777464", "354067037861768", "1671014124932980", "7904396487947504", "37469496390403704" ]
[ "nonn" ]
10
1
2
[ "A378583", "A378584" ]
null
Paul D. Hanna, Jan 10 2025
2025-01-22T04:13:35
oeisdata/seq/A378/A378584.seq
10d18325e0a73f701238f15251835d79
A378585
G.f. A(x) satisfies Sum_{n=-oo..+oo} x^n * (1 - A(x)^n)^(n+2) = 0.
[ "1", "-1", "2", "-7", "24", "-90", "345", "-1373", "5610", "-23418", "99373", "-427370", "1858665", "-8160629", "36123158", "-161033302", "722322008", "-3257737848", "14764170412", "-67202964003", "307090370840", "-1408254347355", "6478788726514", "-29893940649690", "138306656545279", "-641475676394960", "2982029118960410" ]
[ "sign" ]
7
1
3
null
null
Paul D. Hanna, Dec 13 2024
2024-12-14T07:08:51
oeisdata/seq/A378/A378585.seq
51fe2455638b939433d65ed59071ad15
A378586
Number of distinct domination roots among all simple graphs on n vertices.
[ "1", "2", "6", "19", "73", "285", "1554", "10269", "87623", "970975" ]
[ "nonn", "more" ]
5
1
2
null
null
Eric W. Weisstein, Dec 01 2024
2024-12-01T18:47:16
oeisdata/seq/A378/A378586.seq
f06a632de2a22f00812b078d6327b0d2
A378587
Number of distinct chromatic roots among all simple graphs on n vertices.
[ "1", "2", "3", "6", "16", "70", "411", "4085", "76660", "2920668" ]
[ "nonn", "more" ]
5
1
2
null
null
Eric W. Weisstein, Dec 01 2024
2024-12-01T18:47:12
oeisdata/seq/A378/A378587.seq
d706874ae087d0b97f7034cff07ee300
A378588
Triangle read by rows: T(n,k) is the number of maximal chains in the poset of all k-ary words of length <= n, ordered by B covers A iff A_i <= B_{i+k} for all i in A and some k >= 0.
[ "1", "1", "2", "1", "5", "6", "1", "16", "22", "23", "1", "57", "94", "102", "103", "1", "226", "446", "507", "517", "518", "1", "961", "2308", "2764", "2855", "2867", "2868", "1", "4376", "12900", "16333", "17121", "17248", "17262", "17263", "1", "21041", "77092", "103666", "110487", "111739", "111908", "111924", "111925", "1", "106534", "489430", "701819", "761751", "773888", "775758", "775975", "775993", "775994", "1", "563961", "3282956", "5038344", "5578041", "5696293", "5716382", "5719046", "5719317", "5719337", "5719338" ]
[ "nonn", "tabl" ]
27
1
3
[ "A034841", "A143672", "A282698", "A317145", "A378382", "A378588", "A378608" ]
null
John Tyler Rascoe, Dec 01 2024
2025-04-12T20:12:12
oeisdata/seq/A378/A378588.seq
6c25728ed3dc2abd0d84f1772ec9cd59
A378589
Decimal expansion of (1 - 2*A143304)/4.
[ "2", "1", "7", "3", "2", "4", "2", "8", "7", "0", "3", "8", "4", "8", "1", "3", "3", "9", "3", "1", "0", "6", "0", "8", "6", "8", "6", "6", "1", "8", "4", "4", "6", "0", "3", "4", "5", "9", "3", "4", "8", "7", "7", "3", "1", "5", "7", "5", "2", "8", "8", "1", "0", "1", "1", "7", "0", "4", "6", "4", "2", "7", "5", "1", "5", "9", "2", "1", "1", "4", "6", "2", "0", "9", "7", "2", "8", "4", "0", "0", "2", "5", "2", "6", "5", "2", "8", "9", "6", "5", "6", "4", "1", "8", "1", "7", "7", "2", "0", "5" ]
[ "nonn", "cons" ]
4
0
1
[ "A001620", "A002162", "A002388", "A053510", "A074962", "A086237", "A143304", "A225746", "A378589" ]
null
Stefano Spezia, Dec 01 2024
2024-12-03T12:29:17
oeisdata/seq/A378/A378589.seq
6836b8806ff40c5284b87290979bfc24
A378590
Total number of ways to place k nonattacking bishops on an n X n chess board. Triangle T(n,k) read by rows (0 <= k <= 2*n-[n>0]-[n>1]).
[ "1", "1", "1", "1", "4", "4", "1", "9", "26", "26", "8", "1", "16", "92", "232", "260", "112", "16", "1", "25", "240", "1124", "2728", "3368", "1960", "440", "32", "1", "36", "520", "3896", "16428", "39680", "53744", "38368", "12944", "1600", "64", "1", "49", "994", "10894", "70792", "282248", "692320", "1022320", "867328", "389312", "81184", "5792", "128" ]
[ "nonn", "easy", "tabf" ]
24
0
5
[ "A000012", "A000079", "A000290", "A002465", "A172123", "A172124", "A172127", "A172129", "A176886", "A187239", "A187240", "A187241", "A187242", "A201862", "A378590" ]
null
Eder G. Santos, Dec 01 2024
2024-12-28T10:19:37
oeisdata/seq/A378/A378590.seq
ee30bf51f202383fc870dd55ad4a71c5
A378591
Number of edge cuts in the n-Sierpinski gasket graph.
[ "4", "352", "120905728", "2407558186389936749412352", "14134769792236367387238791435785519303295716096758551664972849610340958208" ]
[ "nonn" ]
9
1
1
null
null
Eric W. Weisstein, Dec 01 2024
2024-12-04T18:44:40
oeisdata/seq/A378/A378591.seq
47f3c6890f73042a83e6948158a5ad9c
A378592
a(n) is the first number that is the largest primitive root modulo exactly n numbers.
[ "4", "1", "3", "47", "5" ]
[ "nonn", "more" ]
4
0
1
[ "A306253", "A378592" ]
null
Robert Israel, Dec 01 2024
2024-12-03T12:26:24
oeisdata/seq/A378/A378592.seq
c7b7722b65fc2847310873ed1a39e0db
A378593
Number of squarefree k between consecutive powerful numbers (inclusive).
[ "3", "3", "0", "5", "5", "1", "3", "3", "8", "8", "6", "5", "11", "6", "8", "2", "1", "11", "14", "17", "2", "11", "6", "11", "7", "20", "0", "22", "10", "10", "18", "6", "20", "6", "28", "9", "8", "9", "28", "30", "14", "17", "0", "32", "33", "12", "24", "12", "22", "37", "4", "3", "17", "16", "36", "24", "16", "3", "42", "44", "18", "4", "13", "11", "2", "45", "46", "29", "20", "48", "26", "22", "23" ]
[ "nonn" ]
13
1
1
[ "A001694", "A005117", "A076446", "A240590", "A378593" ]
null
Michael De Vlieger, Dec 09 2024
2024-12-09T23:25:13
oeisdata/seq/A378/A378593.seq
a038b6c6afc5e5ce4d605019893e89a8
A378594
First set of a unique partition of the positive integers into two sets whose distinct pair-sums avoid the Lucas numbers.
[ "1", "4", "5", "8", "9", "11", "12", "15", "16", "19", "22", "23", "26", "27", "29", "30", "33", "34", "37", "40", "41", "44", "45", "48", "51", "52", "55", "56", "58", "59", "62", "63", "66", "69", "70", "73", "74", "76", "77", "80", "81", "84", "85", "87", "88", "91", "92", "95", "98", "99", "102", "103", "105", "106", "109", "110", "113", "116", "117", "120", "121", "124", "127" ]
[ "nonn" ]
11
1
2
[ "A000032", "A378594", "A378595" ]
null
Jeffrey Shallit, Dec 01 2024
2024-12-03T12:30:11
oeisdata/seq/A378/A378594.seq
2a8686188894c2df70907a05ef708db5
A378595
Second set of a unique partition of the positive integers into two sets whose distinct pair-sums avoid the Lucas numbers.
[ "2", "3", "6", "7", "10", "13", "14", "17", "18", "20", "21", "24", "25", "28", "31", "32", "35", "36", "38", "39", "42", "43", "46", "47", "49", "50", "53", "54", "57", "60", "61", "64", "65", "67", "68", "71", "72", "75", "78", "79", "82", "83", "86", "89", "90", "93", "94", "96", "97", "100", "101", "104", "107", "108", "111", "112", "114", "115", "118", "119", "122", "123", "125" ]
[ "nonn" ]
11
1
1
[ "A000032", "A378594", "A378595" ]
null
Jeffrey Shallit, Dec 01 2024
2024-12-03T12:30:22
oeisdata/seq/A378/A378595.seq
ede8e918beb0f549b22ba4007da9daa2
A378596
Möbius transform of A119347, where A119347 number of distinct sums of nonempty subsets of divisors of n.
[ "1", "2", "2", "4", "2", "7", "2", "8", "4", "10", "2", "12", "2", "10", "10", "16", "2", "23", "2", "23", "10", "10", "2", "24", "4", "10", "8", "37", "2", "38", "2", "32", "10", "10", "10", "36", "2", "10", "10", "40", "2", "62", "2", "44", "36", "10", "2", "48", "4", "44", "10", "44", "2", "73", "10", "56", "10", "10", "2", "57", "2", "10", "40", "64", "10", "110", "2", "44", "10", "105", "2", "72", "2", "10", "44", "44", "10", "134", "2", "80", "16", "10", "2", "75", "10", "10", "10" ]
[ "nonn" ]
7
1
2
[ "A008683", "A119347", "A378596", "A378597" ]
null
Antti Karttunen, Dec 02 2024
2024-12-02T15:39:55
oeisdata/seq/A378/A378596.seq
d72d7db07ddcd743b83244ab6af7c03a
A378597
Möbius transform of A378450, where A378450 is the number of positive numbers k <= sigma(n) that are not a sum of any subset of distinct divisors of n.
[ "0", "0", "1", "0", "3", "-1", "5", "0", "5", "0", "9", "0", "11", "4", "5", "0", "15", "-5", "17", "-3", "11", "12", "21", "0", "21", "16", "19", "-9", "27", "-8", "29", "0", "23", "24", "25", "0", "35", "28", "29", "0", "39", "-20", "41", "0", "9", "36", "45", "0", "45", "6", "41", "8", "51", "-19", "45", "0", "47", "48", "57", "3", "59", "52", "23", "0", "55", "-44", "65", "24", "59", "-35", "69", "0", "71", "64", "31", "32", "67", "-56", "77", "0", "65", "72", "81", "9", "75", "76", "77", "-21" ]
[ "sign", "look" ]
10
1
5
[ "A008683", "A119347", "A378450", "A378596", "A378597" ]
null
Antti Karttunen, Dec 02 2024
2024-12-02T17:43:18
oeisdata/seq/A378/A378597.seq
85bad9264328727301e1bdd1308ff2a6
A378598
Parity of A083206, where A083206 is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum.
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
8
1
null
[ "A000035", "A083206", "A179527", "A378449", "A378598", "A378599" ]
null
Antti Karttunen, Dec 03 2024
2024-12-03T11:45:40
oeisdata/seq/A378/A378598.seq
ad302e1237b58e5adeacffb6d06b2b21
A378599
Numbers whose divisors can be partitioned into two disjoint sets with the same sum in an odd number of ways.
[ "6", "12", "20", "24", "28", "30", "48", "56", "60", "70", "80", "88", "90", "96", "104", "140", "156", "168", "176", "180", "192", "208", "210", "216", "224", "234", "252", "270", "272", "280", "300", "304", "312", "320", "336", "350", "352", "360", "368", "384", "396", "408", "420", "432", "448", "464", "468", "476", "480", "496", "504", "532", "550", "552", "560", "612", "630", "644", "650", "696", "700", "720", "728", "736", "760", "768" ]
[ "nonn" ]
13
1
1
[ "A083206", "A083207", "A083209", "A378598", "A378599" ]
null
Antti Karttunen, Dec 03 2024
2024-12-04T15:44:17
oeisdata/seq/A378/A378599.seq
522d80f82d3730b83cb1a814b79e5f7c
A378600
Signed variant of Zumkeller deficiency: a(n) = signum(A033879(n)) * A103977(n).
[ "1", "1", "2", "1", "4", "0", "6", "1", "5", "2", "10", "0", "12", "4", "6", "1", "16", "-1", "18", "0", "10", "8", "22", "0", "19", "10", "14", "0", "28", "0", "30", "1", "18", "14", "22", "-1", "36", "16", "22", "0", "40", "0", "42", "4", "12", "20", "46", "0", "41", "7", "30", "6", "52", "0", "38", "0", "34", "26", "58", "0", "60", "28", "22", "1", "46", "0", "66", "10", "42", "0", "70", "-1", "72", "34", "26", "12", "58", "0", "78", "0", "41", "38", "82", "0", "62", "40", "54", "0", "88", "0", "70" ]
[ "sign" ]
9
1
3
[ "A005100", "A033879", "A083207", "A083211", "A103977", "A156903", "A171641", "A378600" ]
null
Antti Karttunen, Dec 04 2024
2024-12-04T20:54:16
oeisdata/seq/A378/A378600.seq
b69b34714a504e66881581738ce9010f