On the Composition of the Euler Function and the Dedekind Arithmetic Function

Aimin Guo, Huan Liu, Qiyu Yang

Let $I(n)=\frac{\psi (\varphi (n))}{\varphi (\psi (n))}$ and $K(n)=\frac{\psi (\varphi (n))}{\varphi (\varphi (n))}$, where $\varphi (n)$ is Euler's function and $\psi (n)$ is Dedekind's arithmetic function. We obtain the maximal orde…