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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
OFFSET
1,2
COMMENTS
Dirichlet convolution of A000688 with A050361.
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
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Oct 26 2019
STATUS
approved