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?