On the composition of the Euler function and the sum of divisors function
Volume 108 / 2007
Colloquium Mathematicum 108 (2007), 31-51
MSC: 11A25, 11N37, 11N56.
DOI: 10.4064/cm108-1-4
Abstract
Let $H(n) = {\sigma (\phi (n))/\phi (\sigma (n))}$, where $\phi (n)$ is Euler's function and $\sigma (n)$ stands for the sum of the positive divisors of $n$. We obtain the maximal and minimal orders of $H(n)$ as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.
