Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[Moebius] instead.

The function mobius(n) gives the Moebius function of n (lattice of divisors). It returns 1, -1, or 0 depending on the factorization of n. Note that it returns 0 if and only if n has a square factor > 1.

The command with(numtheory,mobius) allows the use of the abbreviated form of this command.

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

$\mathrm{mobius}\left(1\right)$

$1$

$\mathrm{mobius}\left(20\right)$

$0$

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

$1$

$\mathrm{mobius}\left(105\right)$

$\mathrm{-1}$