*This is a repost. I could not get a precise answer on math.SE and cstheory.SE*

Let FACT denote the integer factoring problem: given $n \in \mathbb{N},$ find primes $p_i \in \mathbb{N},$ and integers $e_i \in \mathbb{N},$ such that $n = \prod_{i=0}^{k} p_{i}^{e_i}.$

Let RSA denote the special case of factoring problem where $k=2, e_i=1$ for all $i$. That is, given $n,$ find two primes $p,q,$ such that $n = pq$ or NONE if this factorization does not exist.

Obviously, RSA is an instance of FACT. Is FACT harder than RSA? Given an oracle that solves RSA in polynomial time, could we construct a polynomial time algorithm to solve FACT?