Extremal orders of compositions of certain arithmetical functions

Abstract

We study the exact extremal orders of compositions $f(g(n))$ of certain arithmetical functions, including the functions $\sigma (n)$, $\varphi (n)$, ${\sigma }^{\ast }(n)$ and ${\varphi }^{\ast }(n)$, representing the sum of divisors of $n$, Euler's function and their unitary analogues, respectively. Our results complete, generalize and refine known results.

improved and corrected final version

References in corpus (1)

• The maximal order of a class of multiplicative arithmetical functions