A relation to a remainder terms in an asymptotic formula for the associated Euler totient function

TL;DR

This paper extends Montgomery's relation on error terms to a special case of the associated Euler totient function, providing new insights into its asymptotic behavior.

Contribution

It establishes a Montgomery-type relation for error terms in asymptotic formulas of a generalized Euler totient function.

Findings

Proves a Montgomery-like relation for error terms

Generalizes previous asymptotic results

Enhances understanding of associated Euler totient function

Abstract

H.L.Montgomery proved a relation for error terms in asymptotic formulas for the Euler totient function. J.Kaczorowski defined the associated Euler totient function which generalizes and obtained an asymptotic formula for it. In this paper, we prove a relation on error terms similar to H.L.Montgomery's result for a certain special case of the associated Euler totient function.