Because of the odd nature of my question, I am interested in partial solutions if a complete solution is not known. Specifically, the question I am trying to answer is the following:
Is there a method to show that a number does not have precisely two prime factors if we know it has at most three?
More generally, any condition uniquely satisfied by integers with an odd number of prime factors, or with an even number of prime factors, but not numbers with both, will be extremely helpful.
Edit: As per helpful comments, I am assuming the integer is entirely square free; that is, my question refers to distinct prime factors. (If there is an answer or partial answer that does not refer to specifically distinct prime factors, however, it would still be appreciated).