  We describe an algorithm to compute the essentially different factorizations
of a given image primitive integer-valued polynomial $f(X)=g(X)/d\in\Q[X]$,
where $g\in\Z[X]$ and $d\in\N$ is square-free, assuming that the factorization
of $g(X)$ in $\Z[X]$ and $d$ in $\Z$ is known. We translate this problem into a
combinatorial one.
