Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Bouderbala, Mihoub
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891756670
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