isqrfree - Maple Help

isqrfree

integer square-free factorization

 Calling Sequence isqrfree(n)

Parameters

 n - any integer

Description

 • 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, $\mathrm{gcd}\left({p}_{i},{p}_{j}\right)=1$ for all $i\ne j$, and u is the sign of n. The square-free factorization of n is: $n=u{p}_{1}^{{e}_{1}}\cdots {p}_{m}^{{e}_{m}}$.

Examples

 > $\mathrm{isqrfree}\left(61\right)$
 $\left[{1}{,}\left[\left[{61}{,}{1}\right]\right]\right]$ (1)
 > $\mathrm{isqrfree}\left(180\right)$
 $\left[{1}{,}\left[\left[{5}{,}{1}\right]{,}\left[{6}{,}{2}\right]\right]\right]$ (2)
 > $\mathrm{ifactors}\left(-120\right)$
 $\left[{-1}{,}\left[\left[{2}{,}{3}\right]{,}\left[{3}{,}{1}\right]{,}\left[{5}{,}{1}\right]\right]\right]$ (3)