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arXiv · 2504.12435

On certain sums involving the largest prime factor over integer sequences

Mihoub Bouderbala
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Abstract

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.

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Mihoub Bouderbala. 2025-04-16. On certain sums involving the largest prime factor over integer sequences. https://arxiv.org/abs/2504.12435

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