A098009 Numbers k such that the transient part of the aliquot sequence for k is finite and sets a new record.

1, 2, 4, 9, 12, 30, 102, 138

Offset: 1

Author

N. J. A. Sloane, Sep 10 2004

Keywords

• nonn
• more

Comments

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.

Examples

			138 has a transient of length 177 (see Guy's book).
		

References

• See references and links in A098007, A098008.

Crossrefs

Records in A098008. Cf. A098010.

Programs

Mathematica

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 *)

Extensions

102 and 138 from Robert G. Wilson v, Sep 10 2004