Given a positive integer $n>1$ with prime factorization
$n=\prod_{p_i \text{ prime}}p_i^{k_i}, \space i\ge1, \space k_i \in \mathbb N^*$
how can I compute the number of factorizations of $n$, $\text F(n)$ (multiplications by $1$ are excluded) ?
- $5\times 24$ and $4\times 5\times 6$ are two different factorizations of $120$.
- The prime factorization of a number is of course one of its factorizations.
- $\text F(p) = 0$ for any prime number $p$.
If there is a no formula, an algorithm will be appreciated.