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ON A PROBLEM OF PONGSRIIAM ON THE SUM OF DIVISORS

Part of: Multiplicative number theory Elementary number theory

Published online by Cambridge University Press:  13 September 2024

RUI-JING WANG Open the ORCID record for RUI-JING WANG [Opens in a new window]
RUI-JING WANG*
Affiliation:
School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, PR China
*
e-mail: wangruijing271@163.com
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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].

Keywords

arithmetic functionsmonotonicitysum of divisors function

MSC classification

Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11N25: Distribution of integers with specified multiplicative constraints
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 13 - 18
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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