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

The function sigma(n) will compute the sum of the positive divisors of n.

The function sigma[k](n)  will compute the sum of the kth power of positive divisors of n.

This function is part of the numtheory package, and so can be used in the form sigma[..](..) only after performing the command with(numtheory) or with(numtheory, sigma).  The function sigma(..) can always be accessed in the above form or the long form numtheory[sigma](..).

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

$\mathrm{\sigma }\left(9\right)$

$13$

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

$\left\{1\,2\,4\,5\,10\,20\,25\,50\,100\right\}$

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

$217$

$\mathrm{\sigma }\left[0\right]\left(100\right)$

$9$

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

$9$