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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07931 |
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| _version_ | 1866914801362403328 |
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| author | Wang, Rui-Jing |
| author_facet | Wang, Rui-Jing |
| contents | For any positive integer $n$, let $σ(n)$ be the sum of all positive divisors of $n.$ In this paper, it is proved that for every integer $ 1\leq k\leq 29,\ (k,30)=1, $ we have $$\sum_{n\leq K}σ(30n)>\sum_{n\leq K}σ(30n+k)$$ for all $K\in \mathbb{N},$ which gives a positive answer to a problem posed by Pongsriiam recently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a problem of Pongsriiam on the sum of divisors Wang, Rui-Jing Number Theory For any positive integer $n$, let $σ(n)$ be the sum of all positive divisors of $n.$ In this paper, it is proved that for every integer $ 1\leq k\leq 29,\ (k,30)=1, $ we have $$\sum_{n\leq K}σ(30n)>\sum_{n\leq K}σ(30n+k)$$ for all $K\in \mathbb{N},$ which gives a positive answer to a problem posed by Pongsriiam recently. |
| title | On a problem of Pongsriiam on the sum of divisors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.07931 |