numtheory/sigma(deprecated) - Help

numtheory

 sigma
 sum of divisors

 Calling Sequence sigma(n) sigma[k](n)

Parameters

 k - integer n - integer

Description

 • Important: The numtheory[sigma] command 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](..).

Examples

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $\mathrm{σ}\left(9\right)$
 ${13}$ (1)
 > $\mathrm{divisors}\left(100\right)$
 $\left\{{1}{,}{2}{,}{4}{,}{5}{,}{10}{,}{20}{,}{25}{,}{50}{,}{100}\right\}$ (2)
 > $\mathrm{σ}\left(100\right)$
 ${217}$ (3)
 > $\mathrm{σ}[0]\left(100\right)$
 ${9}$ (4)
 > $\mathrm{τ}\left(100\right)$
 ${9}$ (5)