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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