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.