The maximal order of a class of multiplicative arithmetical functions
László Tóth, Eduard Wirsing
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 σA(n)= Σd∈ A(n) d, where A(n) is a subset of the set of all positive divisors of n, including the divisor-sum function σ(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 ϕ(n) and its unitary analogue.
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