# Weird summation

**Number Theory**Level 5

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. \(\dfrac{df}{ds}=0\)