Arithmetic properties of <em>φ(n)/λ(n)</em> and the structure of the multiplicative group modulo <em>n</em>

Abstract

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