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 A054685 Number of partitions of n into distinct prime powers (1 not considered a power). 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS T. D. Noe and Reinhard Zumkeller, Table of n, a(n) for n = 0..10000, first 1000 terms from T. D. Noe FORMULA G.f.: Prod(p prime, Prod(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 Adjacent sequences:  A054682 A054683 A054684 * A054686 A054687 A054688 KEYWORD nonn AUTHOR David W. Wilson, Apr 19 2000 STATUS approved

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Last modified July 25 12:56 EDT 2021. Contains 346290 sequences. (Running on oeis4.)