The Divisor Sigma Function

maximum integer

100

1000

5000

connect points

include Gaussian integers

y axis

number of divisors

In Mathematica, DivisorSigma[k,n] calculates the sum of the

th

k

powers of the divisors of

n

. For example, you can use DivisorSigma[0,n] in order to determine the number of divisors of the integer

n

and DivisorSigma[1,n] to determine the sum of these divisors. This Demonstration allows you to visualize the results of applying DivisorSigma to various ranges of integers.

When Gaussian integers are selected, the Demonstration returns a plot of the absolute values of DivisorSigma, since the result may be complex.