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A054685
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Number of partitions of n into distinct prime powers (1 not considered a power).
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23
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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
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f.: Product_{p prime} Product_{k >= 1} (1 + x^(p^k)).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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