A096356 - OEIS

%I #9 Mar 28 2015 22:00:08

%S 1,6,12,30,112,24,80,36,228,150,48,156,160,126,1242,132,5300,1330,448,

%T 1326,108,96,1288,90,918,84,1026,750,858,16592,744,72,910,952,60,696,

%U 896,702,690,760,6966,12464,192,570,400,6642,546,594,2178,2420,5424,640

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

%C All numbers in the sequence are pseudoperfect.

%F A033630(a(n))=n; A033630(j)<>n for j<a(n). - _R. J. Mathar_, Dec 11 2006

%e 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.

%t (* 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 *)

%Y Records are in A065218.

%K nonn

%O 0,2

%A _Bernardo Boncompagni_, Aug 04 2004

%E More terms from _Robert G. Wilson v_, Aug 13 2004

%E Definition corrected by _R. J. Mathar_, Nov 27 2006