A328721 Dirichlet g.f.: Product_{p prime, k>=1} (1 + p^(-s*k)) / (1 - p^(-s*k)).

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

Author

Ilya Gutkovskiy, Oct 26 2019

Keywords

• nonn
• mult

Comments

Dirichlet convolution of A000688 with A050361.

Crossrefs

Cf. A000688, A015128, A050361.

Programs

Mathematica

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