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A014648 Number of partitions of n into its divisors with at least one part of size 1.

%I A014648 #15 Apr 07 2015 09:42:23
%S A014648 1,1,1,2,1,5,1,6,3,8,1,33,1,11,11,26,1,66,1,76,15,17,1,378,5,20,18,
%T A014648 136,1,648,1,166,23,26,23,1954,1,29,27,1212,1,1500,1,309,261,35,1,
%U A014648 8600,7,378,35,422,1,2877,35,2803,39,44,1,66129,1,47,461,1626,41,4936
%N A014648 Number of partitions of n into its divisors with at least one part of size 1.
%H A014648 Alois P. Heinz, <a href="/A014648/b014648.txt">Table of n, a(n) for n = 1..10000</a>
%F A014648 Coefficient of x^(n-1) in expansion of 1/Product_{d divides n} (1-x^d). - _Vladeta Jovovic_, Apr 11 2004
%p A014648 with(numtheory):
%p A014648 a:= proc(n) option remember; local b, l; l:= sort([divisors(n)[]]):
%p A014648       b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,
%p A014648              b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))
%p A014648           end; forget(b):
%p A014648       b(n-1, nops(l))
%p A014648     end:
%p A014648 seq(a(n), n=1..100); # _Alois P. Heinz_, Feb 05 2014
%t A014648 a[n_] := a[n] = Module[{b, l}, l = Divisors[n]; b[m_, i_] := b[m, i] = If[m==0, 1, If[i<1, 0, b[m, i-1] + If[l[[i]]>m, 0, b[m-l[[i]], i]]]]; b[n-1, Length[l]]]; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Apr 07 2015, after _Alois P. Heinz_ *)
%Y A014648 Cf. A018818.
%K A014648 nonn
%O A014648 1,4
%A A014648 _Olivier Gérard_