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.

Showing 1-3 of 3 results.

A113286 Numbers k such that S(S(k))=k, with S(n)=sigma(n)/4: 1/4-sociable numbers of order 1 or 2.

Original entry on oeis.org

30240, 32760, 859320, 898560, 2096640, 2178540, 2234232, 23569920, 45532800, 54996480, 61281792, 142990848, 422688000, 436205952, 1379454720
Offset: 1

Views

Author

Yasutoshi Kohmoto, Jan 27 2006

Keywords

Comments

a(1) and a(2) are 4-perfect numbers (A027687). a(4) = S(a(3)).
a(6), a(8), a(9), a(12), and a(15) are also 4-perfect numbers (A027687). - Michel Marcus, Feb 23 2014

Crossrefs

A027687 is a subsequence.
Cf. A113546 (1/3-sociable numbers).
Cf. A355279 (1/4-sociable numbers of order 1 or 3).

Programs

  • PARI
    isok(n) = (type(s= sigma(n)/4) == "t_INT") && (sigma(s)/4 == n); \\ Michel Marcus, Feb 20 2014

Extensions

a(5)-a(15) added by Michel Marcus, Feb 24 2014

A355279 Numbers k such that S(S(S(k))) = k, with S(n) = sigma(n)/4: 1/4-sociable numbers of order 1 or 3.

Original entry on oeis.org

30240, 32760, 2178540, 23569920, 45532800, 46475520, 48933360, 50995620, 60933600, 69995520, 72807696, 142990848
Offset: 1

Views

Author

M. F. Hasler, Sep 25 2022

Keywords

Comments

a(6..11) = { 46475520, 48933360, 50995620, ..., 72807696 } are the first terms not in A027687 (4-perfect numbers), which is obviously a subsequence.
a(11..12) = { 72807696, 142990848 } are the first terms that are not multiples of 60.

Crossrefs

A027687 is a subsequence.
Cf. A113286 (1/4 sociable numbers of order <= 2), A113546 (1/3-sociable numbers).

Programs

  • PARI
    is_A355279(n, f(x)=if(x && x%4==0, sigma(x\4)))= f(f(sigma(n)))==n*4

A356548 Let S(n)=sigma(n)/3. Numbers k such that S^m(k)=k, 1/3-sociable numbers (of any order).

Original entry on oeis.org

120, 672, 7560, 7680, 8064, 8184, 8840, 9600, 10540, 34944, 36576, 38080, 65520, 71680, 75264, 77748, 90272, 472416, 510720, 523776, 605024, 654080, 1100190, 1124352, 14913024, 16149760, 27797760, 33931072, 34012160, 459818240
Offset: 1

Views

Author

Michel Marcus, Aug 11 2022

Keywords

Comments

It appears that, for initial i=660880440, the sequence x->S(x) diverges.
Barring such cases, the next 3 terms would be 775898880, 874897408 and 1476304896.

Examples

			120 -> 120 so 120 is a term, a 3-perfect number.
7680 -> 8184 -> 7680, a group of 2 sociable terms.
7560 -> 9600 -> 10540 -> 8064 -> 8840 -> 7560, a group of 5 sociable terms.
34944 -> 38080 -> 36576 -> 34944, a group of 3 sociable terms.
		

Crossrefs

Subsequences: A005820 (3-perfect), A113546 (1/3-sociable numbers of order 1 and 2).
Showing 1-3 of 3 results.