Let $\Omega$ be prime big omega function. (Here is description-https://en.wikipedia.org/wiki/Prime_omega_function).
Also let $n$ is composite number.
Find as good as you can upper bound of number $\Omega(\prod_{k : \gcd(k,2n)=1}k)$
I tried so far to use theory of $p$-adic numbers and combine with primes that are less than $2n$ and don't divide $2n$ but I have no idea how to solve it.
I hope that you can help me.
Regards.