Is it possible to find an estimate of the summation $$s(n)=\sum_{k=1}^n\frac1{\varphi(k\cdot p_k)}$$ where $\varphi(n)$ is the totient function and $p_k$ the k-th prime?

The corresponding series seems to converge to the value $$\lim_{n\rightarrow\infty}s(n)=1.86491\ldots$$ but I don't see a simple way to prove it.

Many thanks.