I have been looking at this for days and I am going insane. 

I need to show that for a dirichlet series 
equal to $\zeta(s)\zeta(2s)$  the sum of the coefficients less that x is $x\zeta(2)+O(x^(3/4))$ and then expand that to the $\Pi \zeta(ks)$ for all k in an effort to find the formula for the number of non-isomorphic abelian groups. 

I know that using perron's formula there is a simple pole at $s=1$ that gives a residue of $X\zeta(2)$ but I can't find a contour that converges or the exact error term.