Abstract
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].
Publisher
Cambridge University Press (CUP)
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