Arithmetic Function

Let $$f : \mathbb{N} \to \mathbb{N}$$ be a strictly increasing function such that $$f(2) = 2$$ and $$f(ab) = f(a) \cdot f(b)$$ for $$\gcd(a, b) = 1$$.

Evaluate the sum of all possible values of $$f(17)$$.

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