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%I #4 Oct 26 2019 10:02:25
%S 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,
%T 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,
%U 4,8,2,8,4,8,2,32,2,4,8,8,4,8,2,28
%N Dirichlet g.f.: Product_{p prime, k>=1} (1 + p^(-s*k)) / (1 - p^(-s*k)).
%C Dirichlet convolution of A000688 with A050361.
%F a(n) = Sum_{d|n} A000688(n/d) * A050361(d).
%F If n = Product (p_j^k_j) then a(n) = Product (A015128(k_j)).
%t Table[DivisorSum[n, (Times @@ PartitionsP[Last /@ FactorInteger[n/#]]) (Times @@ PartitionsQ[Last /@ FactorInteger[#]]) &], {n, 1, 80}]
%Y Cf. A000688, A015128, A050361.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Oct 26 2019
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