# Weird summation

Let $$\Omega_s(n)$$ be a completely additive function

(i.e. $$\Omega_s(ab)=\Omega_s(a)+\Omega_s(b)$$) satisfying $\Omega_s(p)=p^s$ where $$p$$ is a prime. Then $\sum_{n=1}^\infty \dfrac{\Omega_{-s}(n)}{n^s} =\sum_{n=1}^\infty \dfrac{f(n)}{n^s}$ Find $f(10^{1729})$ Note:

$$f$$ is independent of $$s$$, i.e. $$\dfrac{df}{ds}=0$$

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