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Numbers k such that the transient part of the aliquot sequence for k is finite and sets a new record.
11

%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