The isqrfree function returns the square-free integer factorization of the integer n.

The function returns the result in the form $\left[u\,\left[\left[p_1\,e_1\right]\,\mathrm{...}\,\left[p_m\,e_m\right]\right]\right]$ where $p_i$ is a positive factor of n, $e_i$ is its multiplicity, $\gcd \left(p_i\,p_j\right)=1$ for all $i\ne j$, and u is the sign of n. The square-free factorization of n is: $n\=u{p}_1^{e_1}\cdots p_m^{e_m}$.

$\mathrm{isqrfree}\left(61\right)$

$\left[1\,\left[\left[61\,1\right]\right]\right]$

$\mathrm{isqrfree}\left(180\right)$

$\left[1\,\left[\left[5\,1\right]\,\left[6\,2\right]\right]\right]$

$\mathrm{ifactors}\left(-120\right)$

$\left[\mathrm{-1}\,\left[\left[2\,3\right]\,\left[3\,1\right]\,\left[5\,1\right]\right]\right]$