A096356 Smallest number which can be expressed as the sum of its proper divisors in exactly n ways.

1, 6, 12, 30, 112, 24, 80, 36, 228, 150, 48, 156, 160, 126, 1242, 132, 5300, 1330, 448, 1326, 108, 96, 1288, 90, 918, 84, 1026, 750, 858, 16592, 744, 72, 910, 952, 60, 696, 896, 702, 690, 760, 6966, 12464, 192, 570, 400, 6642, 546, 594, 2178, 2420, 5424, 640

Offset

0,2

Comments

All numbers in the sequence are pseudoperfect.

Links

Table of n, a(n) for n=0..51.

Formula

A033630(a(n))=n; A033630(j)<>n for j<a(n). - R. J. Mathar, Dec 11 2006

Example

a(2)=12 because 12 is the smallest number which can be expressed as the sum of its proper divisors in exactly 2 ways: 12=6+4+2 and 12=6+3+2+1.

Mathematica

(* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Count[Plus @@@ Subsets[ Drop[ Divisors[n], -1]], n]; t = Table[0, {100}]; Do[ a = f[n]; If[a < 101 && t[[a]] == 0, t[[a]] = n; Print[a, " = ", n]], {n, 2, 16600}]; t (* Robert G. Wilson v, Aug 13 2004 *)

Crossrefs

Records are in A065218.

Sequence in context: A073245 A119626 A152522 * A065992 A263587 A085611

Adjacent sequences: A096353 A096354 A096355 * A096357 A096358 A096359

Keyword

nonn

Author

Bernardo Boncompagni, Aug 04 2004

Extensions

More terms from Robert G. Wilson v, Aug 13 2004

Definition corrected by R. J. Mathar, Nov 27 2006

Status

approved