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%I #11 Mar 12 2023 08:48:11
%S 1,2,4,9,12,30,102,138
%N Numbers k such that the transient part of the aliquot sequence for k is finite and sets a new record.
%C In order to extend this there is the problem that there are small numbers (276, 552, etc.) for which it is not presently known if they cycle. I propose that we assume these do not cycle, but mark the records beyond where this becomes an issue as conjectural only.
%D See references and links in A098007, A098008.
%e 138 has a transient of length 177 (see Guy's book).
%t g[n_] := If[n > 0, DivisorSigma[1, n] - n, 0]; f[n_] := NestWhileList[g, n, UnsameQ, All]; a = -1; Do[b = Length[ f[n]] - 1; If[b > a, a = b; Print[n]], {n, 275}] (* _Robert G. Wilson v_, Sep 10 2004 *)
%Y Records in A098008. Cf. A098010.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Sep 10 2004
%E 102 and 138 from _Robert G. Wilson v_, Sep 10 2004
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