The exact series I must show converges absolutely is:
$\sum_{n=1}^{\infty}{\frac{d(n)^r}{n^s}}$
for $s > 1$, $r\in \mathbb{N}$ and where $d(n)=\#\text{ of divisors of } n$. I've been able to show that $d(n)$, $d(n)^r$ are multiplicative and so my series is Dirichlet. As such, I've broken this into Euler sums and thus transformed the series to
$\prod_{P}\left(1 + \frac{d(p)^r}{p^s} + \frac{d(p^2)^r}{p^{2s}} + \cdots\right) = \prod_{P}\sum_{s=0}^{\infty}{\frac{(s+1)^r}{p^s}}$
I'm not sure how to proceed from here. Any help is appreciated, thanks!