부산대학교 도서관

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.
Comment: Submitted (13 pp). This article together with arXiv:1610.04253v4 (published in Acta Arithmetica 194 (2020), 341-366) supersede arXiv:1610.04253v2