The Descartes-Frenicle-Sorli conjecture predicts that $k=1$ if $q^k n^2$ is an odd perfect number with Euler prime $q$. In this note, we present some conditions equivalent to this conjecture.
On inequalities involving counts of the prime factors of an odd perfect number
New techniques for bounds on the total number of Prime Factors of an Odd Perfect Number
The Abundancy Index of Divisors of Odd Perfect Numbers
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