The type( expr, squarefree ) command returns true if expr is a square-free integer, and false otherwise.  An integer is square-free if it is not divisible by the square of any prime number.

An integer is square-free if, and only if, it is equal to its radical.

The type( expr, cubefree ) command returns true if expr is a cube-free integer, and false otherwise.  An integer is cube-free if it is not divisible by the cube of any prime number.

$\mathrm{type}\left(6\,\'\mathrm{squarefree}\'\right)$

$\mathrm{true}$

$\mathrm{type}\left(12\,\'\mathrm{squarefree}\'\right)$

$\mathrm{false}$

$\mathrm{type}\left(12\,\'\mathrm{cubefree}\'\right)$

$\mathrm{true}$

$\mathrm{type}\left(54\,\'\mathrm{cubefree}\'\right)$

$\mathrm{false}$

$N≔100000\:$$\frac{\mathrm{nops}\left(\mathrm{select}\left(\mathrm{type}\,\left[\mathrm{seq}\right]\left(1..N\right)\,\'\mathrm{squarefree}\'\right)\right)}{N}$

$\frac{30397}{50000}$

$\mathrm{evalf}\left(\%\right)$

$\mathrm{lastexception}$

$\mathrm{evalf}\left(\frac{6}{{\mathrm{Pi}}^2}\right)$

$0.6079271016$

$N≔10000\:$$\frac{\mathrm{nops}\left(\mathrm{select}\left(\mathrm{type}\,\left[\mathrm{seq}\right]\left(1..N\right)\,\'\mathrm{cubefree}\'\right)\right)}{N}$

$\frac{8319}{10000}$

$\mathrm{evalf}\left(\%\right)$

$\mathrm{lastexception}$

$\mathrm{evalf}\left(\frac{1}{\mathrm{Zeta}\left(3\right)}\right)$

$0.8319073727$