cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A387163 Numbers k such that sigma(k) >= 3*k and A324644(k)/A324198(k) = 3.

Original entry on oeis.org

10065440, 12794600, 22862840, 24806600, 27399680, 30692480, 33904640, 41629280, 41851040, 46803680, 54625760, 54842480, 70384160, 81915680, 83545280, 87311840, 91571480, 93964640, 95221280, 98030240, 101978240, 103527200, 106719200, 110116160, 121983680, 122904320, 137106200, 137359040, 143195360, 143638880, 144491200
Offset: 1

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Author

Antti Karttunen, Aug 28 2025

Keywords

Comments

This sequence contains all 3-perfect numbers (A005820) that are not multiples of three: 459818240 (= a(99)), 51001180160, and also any such hypothetical triperfects of the form 4u+2, when 2u+1 is not multiple of 3. See comments in A351458.

Links

Crossrefs

Intersection of A023197 and A387161.
Cf. A000203, A005820, A276086, A324198, A324644, A351458.
Cf. also A387165.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A387163(n) = if(sigma(n)<3*n, 0, my(u=A276086(n)); (gcd(sigma(n), u)==3*gcd(n, u)));

Formula

{k | sigma(k) >= 3*k, A324644(k) = 3*A324198(k)}.

A374476 Composite numbers k such that the least prime dividing the sum of divisors of k is equal to the least prime not dividing k.

Original entry on oeis.org

8, 15, 21, 27, 32, 33, 35, 39, 45, 50, 51, 55, 57, 63, 65, 69, 75, 77, 85, 87, 91, 93, 95, 98, 99, 105, 111, 115, 117, 119, 123, 125, 128, 129, 133, 135, 141, 143, 145, 147, 153, 155, 159, 161, 165, 171, 175, 177, 183, 185, 187, 189, 195, 196, 200, 201, 203, 205, 207, 209, 213, 215, 217, 219, 221, 231, 235, 237
Offset: 1

Views

Author

Antti Karttunen, Aug 06 2024

Keywords

Links

Crossrefs

Intersection of A002808 and A374475.
Cf. A000203, A020639, A053669, A374474.
Cf. A228058 (subsequence), and also A324534, A351458, A364286.

Programs

A387161 Numbers k for which A324644(k)/A324198(k) = 3.

Original entry on oeis.org

2, 14, 26, 62, 74, 86, 122, 134, 146, 152, 176, 182, 206, 212, 224, 254, 272, 290, 302, 314, 326, 338, 368, 386, 422, 428, 434, 446, 476, 542, 554, 566, 578, 590, 626, 632, 644, 656, 662, 674, 680, 722, 734, 752, 782, 794, 812, 842, 848, 854, 866, 890, 914, 920, 926, 974, 1046, 1058, 1082, 1088, 1094, 1136, 1154
Offset: 1

Views

Author

Antti Karttunen, Aug 28 2025

Keywords

Links

Crossrefs

Subsequences: A387163 (terms whose abundancy >= 3).
Cf. A000203, A276086, A324198, A324644, A351458.
Cf. also A364286.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A387161(n) = { my(u=A276086(n)); (gcd(sigma(n), u)==3*gcd(n, u)); };
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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