The maximal order of a class of multiplicative arithmetical functions

Abstract

We prove simple theorems concerning the maximal order of a large class of multiplicative functions. As an application, we determine the maximal orders of certain functions of the type ${\sigma }_A(n)={\sum }_{d\in A(n)}d$, where A(n) is a subset of the set of all positive divisors of $n$, including the divisor-sum function $\sigma (n)$ and its unitary and exponential analogues. We also give the minimal order of a new class of Euler-type functions, including the Euler-function $\varphi (n)$ and its unitary analogue.

Cited by in corpus (3)

• On certain arithmetic functions involving exponential divisors
• Regular integers modulo n
• Extremal orders of compositions of certain arithmetical functions