On a sum involving the sum-of-divisors function
type: Item
instance of: scholarly article
title: On a sum involving the sum-of-divisors function
zbMATH Open document ID: 1477.11172
DOI: 10.1155/2021/5574465
author: Feng Zhao
author: Jie Wu
published in: Journal of Mathematics
publication date: 2021-06-25T00:00:00Z
review text: Summary: Let \(\sigma (n)\) be the sum of all divisors of \(n\) and let \([t]\) be the integral part of \(t\). In this paper, we shall prove that \(\sum_{n \leq x} \sigma ([x/n]) = (\pi^2/6)x\log x+O (x(\log x)^{(2/3)} (\log_2 x)^{(4/3)})\) for \(x\longrightarrow\infty\), and that the error term of this asymptotic formula is \(\Omega (x)\).
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 7363424
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5574465
OpenAlex ID: W3151981632
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description: scientific article; zbMATH DE number 7363424