Given an integer $N$ of length $n$ bits, how hard is it to output the number of prime factors (or alternatively number of factors) of $N$?
If we knew the prime factorization of $N$, then this would be easy. However, if we knew the number of prime factors, or the number of general factors, it is not clear how we'd find the actual prime factorization.
Is this problem studied? Are there known algorithms that solve this question without finding the prime factorization?
This question is motivated by curiosity and partially by a math.SE question.