# Lambert series 2, double mersenne summation

Number Theory Level 5

$\large \displaystyle\sum_{p \ \text{prime}} \sum_{k=1}^\infty \dfrac{1}{2^{p^k}-1}= \sum_{n=1}^\infty f(n)2^{-n}$

Let $$f(n)$$ be an additive function satisfying the equation above.

Find $$\large f(10^{12^3})$$.

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