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

0,2

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A328656 A085901 A077224 * A234899 A190553 A270532

Adjacent sequences: A059444 A059445 A059446 * A059448 A059449 A059450

Keyword

nice,nonn

Author

Erich Friedman, Feb 02 2001

Extensions

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

Status

approved