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}$

$\frac{8319}{10000}$

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

$\mathrm{lastexception}$

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

$0.8319073727$