Extremal orders of compositions of certain arithmetical functions
Abstract
Description
We study the exact extremal orders of compositions $f(g(n))$ of certain arithmetical functions, including the functions $σ(n)$, $ϕ(n)$, $σ^*(n)$ and $ϕ^*(n)$, 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
improved and corrected final version