A096258 Number of partitions of n into distinct nonprime parts.

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, 27, 31, 32, 36, 43, 47, 52, 57, 61, 70, 80, 84, 93, 105, 114, 127, 141, 150, 167, 188, 202, 220, 244, 264, 291, 322, 346, 377, 416, 450, 493, 540, 580, 633, 696, 750, 814, 888

Offset: 0

Author

Vladeta Jovovic, Jul 31 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002095.

Cf. A204389.

Programs

Haskell

a096258 = p a018252_list where
   p _      0 = 1
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
-- Reinhard Zumkeller, Jan 15 2012

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+ `if`(i>n or isprime(i), 0, b(n-i, i-1))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..70);  # Alois P. Heinz, May 29 2013

Mathematica

CoefficientList[ Series[ Product[(1 + x^n)/(1 + x^Prime[n]), {n, 70}], {x, 0, 67}], x] (* Robert G. Wilson v, Aug 02 2004 *)

Formula

G.f.: Product_{i>0} (1+x^i)/(1+x^prime(i)).

Extensions

More terms from Robert G. Wilson v, Aug 02 2004