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

The function tau(n) will compute the number of positive divisors of n.

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

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

$\mathrm{divisors}\left(-9\right)$

$\left\{1\,3\,9\right\}$

$\mathrm{\tau }\left(-9\right)$

$3$

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

$\left\{1\right\}$

$\mathrm{\tau }\left(0\right)$

$0$

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

$1$

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

$\left\{1\,2\,4\,5\,10\,20\right\}$

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

$6$

$\mathrm{\sigma }\left[0\right]\left(20\right)$

$6$