Arithmetic properties of $\phi (n)/\lambda (n)$ and the structure of the multiplicative group modulo $n$

Abstract

For a positive integer $n$, we let $\phi (n)$ and $\lambda (n)$ denote the Euler function and the Carmichael function, respectively. We define $\xi (n)$ as the ratio $\phi (n)/\lambda (n)$ and study various arithmetic properties of $\xi (n)$.