Work

On a Problem of Pongsriiam on the Sum of Divisors

Year: 2024

Type: article

Abstract: For any positive integer n, let $\sigma (n)$ be the sum of all positive divisors of n. We prove that for every integer k with $1\leq k\leq 29$ and $(k,30)=1,$ $$ \begin{align*} \sum_{n\leq K}\sigma(30n)>\sum_{n\leq K}\sigma(30n+k) \end{align*} $$ for all $K\in \mathbb {N},$ which gives a positive answer to a problem posed by Pongsriiam [‘Sums of divisors on arithmetic progressions’, Period. Math. Hungar. 88 (2024), 443–460].

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972724000492

Author: RUI-JING WANG

Institution: Jiangsu Second Normal University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

OpenAlex ID: W4402522140

FWCI: 1.121

Cites: 8

Cited by: 1

Related to: 10