New Results for Sorli's Conjecture on Odd Perfect Numbers

Jose Arnaldo B. Dris

Published 2013-02-25, updated 2015-01-09Version 9

If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that $k=1$. In this article, we give a strategy for trying to prove that the inequality $n < q$ is equivalent to this conjecture. We conclude with some remaining open questions regarding $k$ and a conjectured relationship between the divisors $q^k$ and $n$.