New preprint by Dagal and Dris - If $q^k n^2$ is an odd perfect number with special prime $q$, then $k$ is bounded.

Dagal and myself have a new preprint out there, uploaded to the math.GM subject area in arXiv.

Here is the abstract:

In this note, we continue an approach pursued in an earlier paper of the second author and thereby attempt to produce an improved lower bound for the sum $I(q^k) + I(n^2)$, where $q^k n^2$ is an odd perfect number with special prime $q$ and $I(x)$ is the abundancy index of the positive integer $x$.  In particular, this yields an upper bound for $k$.

This paper has already been submitted to a journal for possible publication.