Counting non-prime divisors for large no.s

How do I calculate no. of non-prime divisors of a no. when the no. can vary up to 1e12. For smaller nos. I would have used Pollard rho but it factorizes the no.s (which I don’t want) I just want to count the prime factors, total divisors, and subtract former from latter to get my answer. Now, what algorithm should I use?