Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04018 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $φ(n)$ denote the Euler totient function. In this paper, we first establish a new upper bound for $n/φ(n)$ involving $K(n)$, the function that counts the number of primorials not exceeding $n$. In particular, this leads to an answer to a question raised by Aoudjit, Berkane, and Dusart concerning an upper bound for the sum-of-divisors function $σ(n)$. Furthermore, we give some lower bounds for $N_k/φ(N_k)$ as well as for $σ(N_k)/N_k$, where $N_k$ denotes the $k$th primorial.