The distribution of $\mathrm{gcd}(n,\varphi(n))$

Let $\varphi (n)$ denote Euler’s phi function. We study the distribution of the numbers $(n,\varphi (n))$ and their divisors. Our results generalize previous results of Erdős (1948) and Pollack (2022).

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Publication Details

Journal
Acta Arithmetica
Published
2025-01-01
DOI
https://doi.org/10.4064/aa240725-4-2
Primary Topic
Analytic Number Theory Research
Type
article
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article

The distribution of $\mathrm{gcd}(n,\varphi(n))$

Joshua Stucky
Acta Arithmetica
Analytic Number Theory Research
article

The distribution of $\mathrm{gcd}(n,\varphi(n))$

Joshua Stucky
article en

Abstract

Let $\varphi (n)$ denote Euler’s phi function. We study the distribution of the numbers $(n,\varphi (n))$ and their divisors. Our results generalize previous results of Erdős (1948) and Pollack (2022).

Acta ArithmeticaVol. 219(2)
Georgia Institute of Technology (US)
Openalex Percentile: Top 90%
Analytic Number Theory Research
DOISourceOpenAlex
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