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arXiv · 2108.07697

On the quantity $I(q^k) + I(n^2)$ where $q^k n^2$ is an odd perfect number -- Part II

Keneth Adrian Precillas Dagal·Jose Arnaldo Bebita Dris
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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 $k$.

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Keneth Adrian Precillas Dagal, Jose Arnaldo Bebita Dris. 2021-08-05. On the quantity $I(q^k) + I(n^2)$ where $q^k n^2$ is an odd perfect number -- Part II. https://arxiv.org/abs/2108.07697

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