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%I #9 Jul 24 2017 12:35:20
%S 12,18,20,24,30,102,120,138
%N Numbers n that have a record maximum (> n) in their aliquot sequence.
%C Maximum term in the aliquot sequence of n is considered only if it is larger than n.
%C The record values are in A290142.
%e The aliquot sequence of 30 is: 30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1. The maximum is 259 which is larger than 30, and larger than the maxima of all the aliquot sequences of the numbers below 30.
%t g[n_] := If[n > 0, DivisorSigma[1, n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; seq = {}; a = -1; seq = {}; Do[b = Max[Drop[f[n], 1]]; If[b > a, a = b; AppendTo[seq, n]], {n, 2, 275}]; seq (* after _Robert G. Wilson v_ at A098009 *)
%Y Cf. A098008, A098009, A098010, A290142.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Jul 21 2017