denote by $\zeta_{p}(s)$ the Prime Zeta Function. Now, consider the infinite sum: $D(s)=\sum_{n=0}^{\infty}\zeta_{p}(s)^{n}=\frac{1}{1-\zeta_{p}(s)}\;\;\;\left | \zeta_{p}(s)\right|<1$ $D(s)$ could be thought of as a Dirichlet series in some half plane of convergence : $D(s)=\sum_{n=1}^{\infty}\frac{a_{n}}{n^{s}}$ Using the fundamental theorem of arithmetic, we can prove that: $a_{n}\neq 0,\forall n\in \mathbb{Z}^{+}$ Now, I'm having a hard time making sense of the coefficients $a_{n}$. In particular, they seem to bear some interesting arithmetical information with respect to the factorization of their corresponding indices. I have the feeling that I'm missing something basic !!
Any insights on the numbers $a_{n}$ are appreciated.