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ON A PROBLEM OF PONGSRIIAM ON THE SUM OF DIVISORS
Published online by Cambridge University Press: 13 September 2024
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].
MSC classification
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
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