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A328721 Dirichlet g.f.: Product_{p prime, k>=1} (1 + p^(-s*k)) / (1 - p^(-s*k)). 0
1, 2, 2, 4, 2, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 14, 2, 8, 2, 8, 4, 4, 2, 16, 4, 4, 8, 8, 2, 8, 2, 24, 4, 4, 4, 16, 2, 4, 4, 16, 2, 8, 2, 8, 8, 4, 2, 28, 4, 8, 4, 8, 2, 16, 4, 16, 4, 4, 2, 16, 2, 4, 8, 40, 4, 8, 2, 8, 4, 8, 2, 32, 2, 4, 8, 8, 4, 8, 2, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet convolution of A000688 with A050361.

LINKS

Table of n, a(n) for n=1..80.

FORMULA

a(n) = Sum_{d|n} A000688(n/d) * A050361(d).

If n = Product (p_j^k_j) then a(n) = Product (A015128(k_j)).

MATHEMATICA

Table[DivisorSum[n, (Times @@ PartitionsP[Last /@ FactorInteger[n/#]]) (Times @@ PartitionsQ[Last /@ FactorInteger[#]]) &], {n, 1, 80}]

CROSSREFS

Cf. A000688, A015128, A050361.

Sequence in context: A085191 A188581 A318316 * A165872 A061142 A318312

Adjacent sequences:  A328718 A328719 A328720 * A328722 A328723 A328724

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Oct 26 2019

STATUS

approved

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Last modified August 11 06:20 EDT 2020. Contains 336422 sequences. (Running on oeis4.)