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

Author

Bernardo Boncompagni, Aug 04 2004

Keywords

• nonn

Comments

All numbers in the sequence are pseudoperfect.

Examples

			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.
		

Crossrefs

Records are in A065218.

Programs

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 *)

Formula

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

Extensions

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

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