Abstract
Abstract Motivated by the works of Erdös, Wirsing, 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 $\ell \gt 1$ is a real number and $k: [1, \infty) \rightarrow (0, \infty)$ is an increasing and unbounded function.
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