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

0,10

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A002095.

Cf. A204389.

Sequence in context: A365159 A358639 A358640 * A049879 A053812 A177865

Adjacent sequences: A096255 A096256 A096257 * A096259 A096260 A096261

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 31 2004

Extensions

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

Status

approved