On the composition of the Euler function and the Dedekind arithmetic function

Let [Formula: see text] and [Formula: see text], where [Formula: see text] is Euler’s function and [Formula: see text] is Dedekind’s arithmetic function. We obtain the maximal order of [Formula: see text], as well as the average orders of [Formula: see text] and [Formula: see text]. Furthermore, we prove a density theorem for both [Formula: see text] and [Formula: see text].

Authors

Huan Liu (ORCID: https://orcid.org/0000-0002-8674-0901)
Aimin Guo (ORCID: https://orcid.org/0009-0007-3812-5780)
Qiyu Yang (ORCID: https://orcid.org/0000-0001-5700-8685)
Xiao Peng (ORCID: https://orcid.org/0000-0003-1971-6298)

Institutions

Macau University of Science and Technology (MO)
Henan Normal University (CN)

Publication Details

Journal: International Journal of Number Theory
Published: 2025-12-11
DOI: https://doi.org/10.1142/s1793042126500454
Primary Topic: Analytic Number Theory Research
Type: article
Field-Weighted Citation Impact: 0.00

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article

On the composition of the Euler function and the Dedekind arithmetic function

Huan Liu, Aimin Guo, Qiyu Yang, Xiao Peng

Dec 11, 2025

International Journal of Number Theory

Analytic Number Theory Research

article

On the composition of the Euler function and the Dedekind arithmetic function

Huan Liu, Aimin Guo, Qiyu Yang, Xiao Peng

December 11, 2025article en

Abstract

Let [Formula: see text] and [Formula: see text], where [Formula: see text] is Euler’s function and [Formula: see text] is Dedekind’s arithmetic function. We obtain the maximal order of [Formula: see text], as well as the average orders of [Formula: see text] and [Formula: see text]. Furthermore, we prove a density theorem for both [Formula: see text] and [Formula: see text].

International Journal of Number TheoryVol. 22(04)

Macau University of Science and Technology (MO), Henan Normal University (CN)

Openalex Percentile: Top 54%

Analytic Number Theory Research

DOI Source OpenAlex

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