A059447 Smallest number that takes n steps to get to 1 under the map f(n)=sigma(n)-n, the sum of the proper divisors.

1, 2, 4, 9, 14, 16, 12, 34, 52, 90, 60, 66, 54, 42, 30, 126, 114, 102, 624, 760, 680, 580, 540, 748, 740, 520, 672, 408, 666, 360, 264, 546, 510, 330, 318, 2960, 2574, 1782, 1494, 3672, 3114, 2790, 1680, 1386, 1374, 930, 612, 594, 582, 378, 366, 180, 3570

Offset: 0

Author

Erich Friedman, Feb 02 2001

Keywords

• nice
• nonn

Examples

			a(4)=14 since 14->10->8->7->1 and no smaller number takes 4 steps.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A003023 (length of aliquot sequence for n).

Programs

Mathematica

f[n_] := DivisorSigma[1, n] - n; f[1] = 1; a[n_] := Catch[For[k = 1, True, k++, nl = NestList[f, k, n]; p = Position[nl, 1, 1, 1]; If[p != {}, If[p[[1, 1]] - 1 == n, Throw[k]]]]]; Table[a[n], {n, 0, 52}] (* Jean-François Alcover, Feb 01 2013 *)

Extensions

More terms from T. D. Noe, Nov 27 2006