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A280586 Expansion of Product_{p prime, k>=2} 1/(1 - x^(p^k)). 2
1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 4, 2, 1, 0, 4, 2, 1, 0, 6, 5, 2, 2, 6, 5, 2, 2, 10, 8, 5, 4, 12, 8, 5, 4, 16, 14, 8, 9, 18, 16, 8, 9, 24, 23, 15, 14, 30, 25, 18, 14, 36, 36, 26, 25, 42, 42, 29, 28, 52, 54, 42, 40, 65, 60, 50, 43, 78, 78, 65, 63, 93, 92, 73, 72, 110, 117, 96, 94, 135, 133, 114, 103, 158, 166, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Number of partitions of n into proper prime powers (A246547).

LINKS

Table of n, a(n) for n=0..90.

Eric Weisstein's World of Mathematics, Prime Power

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{p prime, k>=2} 1/(1 - x^(p^k)).

EXAMPLE

a(16) = 4 because we have [16], [8, 8], [8, 4, 4] and [4, 4, 4, 4].

MATHEMATICA

nmax = 90; CoefficientList[Series[Product[1/(1 - Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k), {k, 2, nmax}], {x, 0, nmax}], x]

PROG

(PARI) x='x+O('x^68); Vec(prod(k=2, 67, 1/(1 - sign(bigomega(k) - 1) * (1\omega(k)) * x^k))) \\ Indranil Ghosh, Apr 03 2017

CROSSREFS

Cf. A023893, A023894, A246547.

Sequence in context: A072575 A025872 A280125 * A112344 A294080 A294019

Adjacent sequences:  A280583 A280584 A280585 * A280587 A280588 A280589

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 06 2017

STATUS

approved

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Last modified July 8 02:24 EDT 2020. Contains 335503 sequences. (Running on oeis4.)