A113286 -id:A113286 - cp's OEIS frontend

A113546 Let S(n)=sigma(n)/3. Numbers k such that S(S(k))=k, 1/3-sociable number of order 1 or 2.

120, 672, 7680, 8184, 523776, 1100190, 1124352, 14913024, 16149760, 459818240, 775898880, 874897408, 1476304896, 51001180160

Offset: 1

Yasutoshi Kohmoto, Jan 27 2006

a(1), a(2), a(5) and a(10) are 3-perfect numbers (A005820). [Corrected by Mauro Fiorentini, Jul 21 2015]
a(4) = S(a(3)).
a(15) > 1.5*10^11. - Giovanni Resta, Jul 21 2015

Eric Weisstein's World of Mathematics, Sociable Numbers

A005820 is a subsequence.

Cf. A113286 (1/4-sociable numbers of order 1 or 2).

isok(n) = (type(s=sigma(n)/3) == "t_INT") && (sigma(s)/3 == n); \\ Michel Marcus, Feb 20 2014

a(6)-a(9) from Michel Marcus, Feb 20 2014
a(10)-a(12) from Michel Marcus, Feb 24 2014
a(13)-a(14) from Giovanni Resta, Jul 22 2015

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

M. F. Hasler, Sep 25 2022

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.

Eric Weisstein's World of Mathematics, Sociable Numbers

A027687 is a subsequence.

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

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

cp's OEIS Frontend

A113546 Let S(n)=sigma(n)/3. Numbers k such that S(S(k))=k, 1/3-sociable number of order 1 or 2.

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