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arXiv · 2406.06892

On the Within-perfect Numbers

Chung-Hang Kwan·Steven J. Miller
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Abstract

Motivated by the works of Erd\"os, Pomerance, Wolke and Harman on the sum-of-divisor function $\sigma(n)$, we study the distribution of a special class of natural numbers closely related to (multiply) perfect numbers which we term `$(\ell;k)$-within-perfect numbers', where $\ell >1$ is a real number and $k: [1, \infty) \rightarrow (0, \infty)$ is an increasing and unbounded function.

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Chung-Hang Kwan, Steven J. Miller. 2024-06-11. On the Within-perfect Numbers. https://arxiv.org/abs/2406.06892

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