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A096258
Number of partitions of n into distinct nonprime parts.
24
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
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jul 31 2004
EXTENSIONS
More terms from Robert G. Wilson v, Aug 02 2004
STATUS
approved