On the average value of the first $ n $ values of the sum-of-divisors function
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 165-172
MSC: Primary 11N37.
DOI: 10.4064/cm8814-7-2022
Published online: 16 November 2022
Abstract
We prove that the number of positive integers $ n \leq x $ dividing $ \sigma (1) + \cdots + \sigma (n)$ is less than $x/(\log x)^{0.15742} $ for all sufficiently large $ x $, where $ \sigma $ stands for the sum-of-divisors function.
