Firstly, let me divulge. I've been doing a lot of research on the summation of two coprime numbers and unfortunately have failed to come up with the properties I'm seeking; it is my hope that someone here might be of some help.

Let $(j, k)\in \mathbb{N}^2$ be coprime.

Can $\Omega(j + k)$ or $\omega(j + k)$ be expressed as some function of $\omega(j)$, $\omega(k)$, $\lambda(j)$, $\lambda(k)$, $ j$, and/or $k$?

If not, then maybe for the special case that $(j, k)$ are prime, or in particular, odd primes?

If the answer is still no, any information regarding this topic is much appreciated.

Note: The functions $\Omega$, $\omega$, and $\lambda$, are the total prime factors, distinct prime factors, and the Liouville function respectively.