A355279 - OEIS

%I #9 Sep 26 2022 20:18:54

%S 30240,32760,2178540,23569920,45532800,46475520,48933360,50995620,

%T 60933600,69995520,72807696,142990848

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

%C a(6..11) = { 46475520, 48933360, 50995620, ..., 72807696 } are the first terms not in A027687 (4-perfect numbers), which is obviously a subsequence.

%C a(11..12) = { 72807696, 142990848 } are the first terms that are not multiples of 60.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>

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

%Y A027687 is a subsequence.

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

%K nonn,more

%O 1,1

%A _M. F. Hasler_, Sep 25 2022