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Power Values of Divisor Sums

Frits Beukers, Florian Luca and Frans Oort
The American Mathematical Monthly
Vol. 119, No. 5 (May 2012), pp. 373-380
DOI: 10.4169/amer.math.monthly.119.05.373
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Page Count: 8
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Power Values of Divisor Sums
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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.

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