In the parent article there has been proved the formula
It follows that the sum of the ’th powers of those divisors is given by
This complex function of is called divisor function (http://planetmath.org/DivisorFunction). The equation (1) may be written in the form
usable also for . For the special case of one prime power the function consists of the single geometric sum (http://planetmath.org/GeometricSeries)
which particularly gives when , i.e. when is a multiple of .
A special case of the function (1) is the function (http://planetmath.org/TauFunction) of :