The Landau function g(n) is defined to be the largest order of a permutation of degree n, where n is a positive integer.

The Landau(n) command computes the value of g(n).

$\mathrm{with}\left(\mathrm{NumberTheory}\right)\:$

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$\mathrm{Landau}\left(3\right)$

$3$

$\max \left(\mathrm{map}\left(\mathrm{PermOrder}\,\mathrm{Elements}\left(\mathrm{Symm}\left(3\right)\right)\right)\right)$

$3$

$\mathrm{Landau}\left(10\right)$

$30$

$\mathrm{Landau}\left(100\right)$

$232792560$

The NumberTheory[Landau] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.