On certain sums involving the largest prime factor over integer sequences
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914366603919360 |
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| author | Bouderbala, Mihoub |
| author_facet | Bouderbala, Mihoub |
| contents | Given an integer $n \ge 2$, its prime factorization is expressed as $n= \prod_{i=1}^s p_i^{a_i}$. We define the function $f(n)$ as the smallest positive integer such that $f(n)!$ is divisible by $n$. The main objective of this paper is to derive an asymptotic formula for both sums $\sum_{n \le x} f(n)$ and $\sum_{n \le x, n \in S_k} f(n)$, where $S_k$ denotes the set of all $k$-free integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On certain sums involving the largest prime factor over integer sequences Bouderbala, Mihoub Number Theory 11A05, 11N37 Given an integer $n \ge 2$, its prime factorization is expressed as $n= \prod_{i=1}^s p_i^{a_i}$. We define the function $f(n)$ as the smallest positive integer such that $f(n)!$ is divisible by $n$. The main objective of this paper is to derive an asymptotic formula for both sums $\sum_{n \le x} f(n)$ and $\sum_{n \le x, n \in S_k} f(n)$, where $S_k$ denotes the set of all $k$-free integers. |
| title | On certain sums involving the largest prime factor over integer sequences |
| topic | Number Theory 11A05, 11N37 |
| url | https://arxiv.org/abs/2504.12435 |