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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.
4
51, 72, 120, 132, 672, 2602, 4756, 10054, 14884, 45840, 51168, 116252, 523776, 906202, 3003698, 5271836, 65071776, 77260656, 82842816, 89761152, 138357404, 139626548, 459818240, 985948800, 1381340160, 1476304896, 1489384608, 2183133696, 3835877062
OFFSET
1,1
COMMENTS
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,...
LINKS
Eric Weisstein's World of Mathematics, Sociable Numbers
EXAMPLE
{51,-30,132,72} is a {2,1}-Aliquot cycle.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Yasutoshi Kohmoto, Jan 27 2006
EXTENSIONS
a(12)-a(22) from Robert G. Wilson v, Jan 30 2006
a(23)-a(29) from Charles R Greathouse IV, Nov 13 2010
STATUS
approved