# On two functions arising in the study of the Euler and Carmichael quotients

## TL;DR

This paper studies two arithmetic functions linked to Euler and Carmichael quotients, exploring their relationships, frequency of vanishing, and typical and extreme values to deepen understanding of these quotients.

## Contribution

It introduces and analyzes two functions related to Euler and Carmichael quotients, revealing their properties and behaviors in new ways.

## Key findings

- Identified relations between the two functions.
- Characterized the frequency of vanishing of the functions.
- Described typical and extreme value behaviors.

## Abstract

We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.