cp's OEIS Frontend

A113285 Let S(n)=sigma(|n|)-2*n; sequence gives numbers n such that S(S(S(S(n))))=n. May be called {2,1}-Sociable number of orders 1 or 2 or 4.

%I A113285 #15 Feb 16 2025 08:32:59
%S A113285 51,72,120,132,672,2602,4756,10054,14884,45840,51168,116252,523776,
%T A113285 906202,3003698,5271836,65071776,77260656,82842816,89761152,138357404,
%U A113285 139626548,459818240,985948800,1381340160,1476304896,1489384608,2183133696,3835877062
%N A113285 Let S(n)=sigma(|n|)-2*n; sequence gives numbers n such that S(S(S(S(n))))=n. May be called {2,1}-Sociable number of orders 1 or 2 or 4.
%C A113285 Orders of cycles are 4,4,1,4,1,4,4,4,4,2,2,2,1,2,4,4,4,4,4,4,4,4,...
%H A113285 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>
%e A113285 {51,-30,132,72} is a {2,1}-Aliquot cycle.
%t A113285 fQ[n_] := Nest[ DivisorSigma[1, # ] - 2# &, n, 4] == n; t = {}; Do[ If[ fQ[n], AppendTo[t, n]], {n, 3*10^7}]; t (* _Robert G. Wilson v_ *)
%Y A113285 Cf. A113791, A114528, A114529.
%K A113285 nonn
%O A113285 1,1
%A A113285 _Yasutoshi Kohmoto_, Jan 27 2006
%E A113285 a(12)-a(22) from _Robert G. Wilson v_, Jan 30 2006
%E A113285 a(23)-a(29) from _Charles R Greathouse IV_, Nov 13 2010