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A096258 Number of partitions of n into distinct nonprime parts.

%I A096258 #12 Jul 25 2015 19:34:17
%S A096258 1,1,0,0,1,1,1,1,1,2,3,2,2,3,4,5,5,4,6,8,8,9,11,11,13,16,17,19,22,23,
%T A096258 27,31,32,36,43,47,52,57,61,70,80,84,93,105,114,127,141,150,167,188,
%U A096258 202,220,244,264,291,322,346,377,416,450,493,540,580,633,696,750,814,888
%N A096258 Number of partitions of n into distinct nonprime parts.
%H A096258 Alois P. Heinz, <a href="/A096258/b096258.txt">Table of n, a(n) for n = 0..1000</a>
%F A096258 G.f.: Product_{i>0} (1+x^i)/(1+x^prime(i)).
%p A096258 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A096258        b(n, i-1)+ `if`(i>n or isprime(i), 0, b(n-i, i-1))))
%p A096258     end:
%p A096258 a:= n-> b(n$2):
%p A096258 seq(a(n), n=0..70);  # _Alois P. Heinz_, May 29 2013
%t A096258 CoefficientList[ Series[ Product[(1 + x^n)/(1 + x^Prime[n]), {n, 70}], {x, 0, 67}], x] (* _Robert G. Wilson v_, Aug 02 2004 *)
%o A096258 (Haskell)
%o A096258 a096258 = p a018252_list where
%o A096258    p _      0 = 1
%o A096258    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
%o A096258 -- _Reinhard Zumkeller_, Jan 15 2012
%Y A096258 Cf. A002095.
%Y A096258 Cf. A204389.
%K A096258 easy,nonn
%O A096258 0,10
%A A096258 _Vladeta Jovovic_, Jul 31 2004
%E A096258 More terms from _Robert G. Wilson v_, Aug 02 2004