The size of the largest cyclic group generated by $g^i\mathbf{mod}n$ is given by CarmichaelLambda(n).

Alternatively, CarmichaelLambda(n) is the smallest integer $i$ such that for all $g$ coprime to $n$, $g^i$ is congruent to $1$ modulo $n$.

lambda is an alias for CarmichaelLambda.

You can enter the command lambda using either the 1-D or 2-D calling sequence. For example, lambda(8) is equivalent to $\mathrm{\lambda }\left(8\right)$.

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

$\mathrm{seq}\left(\mathrm{Totient}\left(i\right)\,i=1..7\right)$

$1,1,2,2,4,2,6$

$\mathrm{seq}\left(\mathrm{CarmichaelLambda}\left(i\right)\,i=1..7\right)$

$1,1,2,2,4,2,6$

$\mathrm{CarmichaelLambda}\left(8\right)$

$2$

$\mathrm{Totient}\left(8\right)$

$4$

$\mathrm{\lambda }\left(21\right)$

$6$

$\mathrm{Totient}\left(21\right)$

$12$

$\mathrm{CarmichaelLambda}\left(k\right)$

$\mathrm{CarmichaelLambda}\left(k\right)$

$d≔\mathrm{CarmichaelLambda}\left(112\right)$

$d≔12$

$\left\{\mathrm{seq}\left(\mathrm{`if`}\left(\mathrm{igcd}\left(g\,112\right)=1\,g^d\mathbf{mod}112\,\mathrm{NULL}\right)\,g=1..111\right)\right\}$

$\left\{1\right\}$

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

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