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So a while back I was on the internet and had encountered a website containing an experimental search for identities for $\pi$. My memory was that the page belonged to either Jonathan Sondow or ...

Richard Mathar $[1]\& [2]$ shows that \begin{align} &\zeta_{2}(s)\equiv\prod_{\Omega(n)=2}^{}\left(\dfrac{1}{1 - n^{s}}\right)^{-1}=\exp \left(\sum _{k=1}^n \frac{P(k s)^2+P(2 k s)}{2 k}\right)...