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A054685
Number of partitions of n into distinct prime powers (1 not considered a power).
23
1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 7, 7, 10, 9, 12, 12, 15, 15, 18, 19, 22, 24, 26, 30, 32, 36, 39, 43, 48, 51, 57, 61, 68, 73, 79, 87, 93, 103, 108, 121, 127, 140, 148, 162, 173, 187, 200, 215, 232, 247, 266, 283, 306, 324, 348, 371, 397, 423, 450, 480, 512, 543, 579, 614
OFFSET
0,6
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (first 1000 terms from T. D. Noe)
FORMULA
G.f.: Product_{p prime} Product_{k >= 1} (1 + x^(p^k)).
MATHEMATICA
CoefficientList[Series[Product[Product[1 +x^(Prime[n]^k), {k, 1, 9}], {n, 1, 25}], {x, 0, 100}], x] (* G. C. Greubel, May 09 2019 *)
PROG
(Haskell)
import Data.MemoCombinators (memo2, integral)
a054685 n = a054685_list !! n
a054685_list = map (p' 2) [0..] where
p' = memo2 integral integral p
p _ 0 = 1
p k m = if m < pp then 0 else p' (k + 1) (m - pp) + p' (k + 1) m
where pp = a000961 k
-- Reinhard Zumkeller, Nov 23 2015
CROSSREFS
Cf. A051613.
Cf. A106244.
Cf. A000961.
Sequence in context: A005044 A266755 A029142 * A286220 A246581 A143619
KEYWORD
nonn
AUTHOR
David W. Wilson, Apr 19 2000
STATUS
approved