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## Multiplicative function

Let $f: \mathbb{N}^*\to \mathbb{N}^*$ a function with the property that $f(m\cdot n)=f(n)\cdot f(m),\ \forall m,n \in \mathbb{N}^*$, for which $f(p_n)=n+1$, for $n \geq 1$, where $p_n$ is the $n$-th prime number. Prove that $\displaystyle \sum_{n=1}^\infty \frac{1}{f^2(n)}=2$.