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.

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

Author

Yasutoshi Kohmoto, Jan 27 2006

Keywords

• nonn

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,...

Examples

			{51,-30,132,72} is a {2,1}-Aliquot cycle.
		

Links

• Eric Weisstein's World of Mathematics, Sociable Numbers

Crossrefs

Cf. A113791, A114528, A114529.

Programs

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 *)

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