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%I #14 Apr 19 2016 01:16:08
%S 51,72,120,132,672,2602,4756,10054,14884,45840,51168,116252,523776,
%T 906202,3003698,5271836,65071776,77260656,82842816,89761152,138357404,
%U 139626548,459818240,985948800,1381340160,1476304896,1489384608,2183133696,3835877062
%N 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>
%e {51,-30,132,72} is a {2,1}-Aliquot cycle.
%t 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 Cf. A113791, A114528, A114529.
%K nonn
%O 1,1
%A _Yasutoshi Kohmoto_, Jan 27 2006
%E a(12)-a(22) from _Robert G. Wilson v_, Jan 30 2006
%E a(23)-a(29) from _Charles R Greathouse IV_, Nov 13 2010
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