I've been reading up a lot Prime Factorization and it's complexity, including a fair number of questions on this very site. However, I still feel there is a question still left unanswered.

So, basically, there is the "Decision Variant" of the *Integer Factorization Problem*, as it's officially known, as well as the "Function Variant". The "Decision Variant" simply asks whether a given integer n has a factor greater than 1.
The "Function Variant", on the other hand, concerns itself with actually finding the Prime Factors if there is more than 1 (it being equivalent to the "Decision Variant" if the answer to that is 'no').

When the question is asked *"In what complexity class does Integer Factorization lie"*, the answer given is usually along the lines of: *"The Decision Variant is both in NP and in Co-NP"*. That is great to know, but that question has been answered and does therefore not need answering again. I will therefore make my Question more specific.

**Question:**
*Is it known in what Complexity Class the "Function Variant" of the Integer Factorization Problem, aka the Prime Factorization Problem, lies? If so, what class would that be?*