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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.

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