|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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):
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|