I'm not sure if this is the right forum for this question, but it seems the best fit to me. The question is as follows:
Neglecting issues of the region of convergence, how does one prove the Dirichlet series generating function
,
where is the sum of the a-th powers of the divisors of n.
I suspect that Dirichlet convolution figures in the solution, but am not sure how to apply it.
--Kevin C.