Type: Article

Power values of divisor sums

Frits Beukers; Florian Luca; Frans Oort;

Abstract:

We consider positive integers whose sum of divisors is a perfect power. This problem had already caught the interest of mathematicians from the 17th century like Fermat, Wallis, and Frenicle. In this article we study this problem and some variations. We also give an example of a cube, larger than one, whose sum of divisors is again a cube.