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A341154 Number of partitions of 2*n into exactly n prime powers (including 1). 1
1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 42, 58, 71, 94, 116, 151, 182, 234, 282, 354, 424, 528, 627, 773, 914, 1113, 1311, 1585, 1854, 2227, 2599, 3095, 3597, 4262, 4931, 5811, 6704, 7855, 9035, 10542, 12080, 14036, 16047, 18561, 21161, 24397, 27736, 31866 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..48.

FORMULA

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

MATHEMATICA

nmax = 48; CoefficientList[Series[Product[1/(1 - Boole[PrimePowerQ[k + 1]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d Boole[PrimePowerQ[d + 1]], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]

CROSSREFS

Cf. A000961, A023893, A181062, A280954, A341153.

Sequence in context: A087750 A341131 A288253 * A035959 A036801 A035966

Adjacent sequences:  A341151 A341152 A341153 * A341155 A341156 A341157

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 06 2021

STATUS

approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)