On near-perfect numbers
Volume 144 / 2016
Colloquium Mathematicum 144 (2016), 157-188
MSC: Primary 11A25.
DOI: 10.4064/cm6588-10-2015
Published online: 3 March 2016
Abstract
For a positive integer $n$, let $\sigma (n)$ denote the sum of the positive divisors of $n$. We call $n$ a near-perfect number if $\sigma (n) = 2n + d$ where $d$ is a proper divisor of $n$. We show that the only odd near-perfect number with four distinct prime divisors is $3^4\cdot 7^2\cdot 11^2\cdot 19^2$.
