The range of the sum-of-proper-divisors function
Volume 168 / 2015
Acta Arithmetica 168 (2015), 187-199
MSC: Primary 11A25; Secondary 11N37.
DOI: 10.4064/aa168-2-6
Abstract
Answering a question of Erdős, we show that a positive proportion of even numbers are in the form $s(n)$, where $s(n)=\sigma (n)-n$, the sum of proper divisors of $n$.
