On An Inequality about Euler’s totient function

descriptionPublicationkeyboard_double_arrow_right Article 19 Sep 2024Publisher:ScienceOpenJournal:Notes on Number Theory and Discrete Mathematics, volume 31, pages 299-304 (issn: 1310-5132, eissn: 2367-8275,

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Authors: Cheng-Ting Wang;

doi: 10.14293/pr2199.001078.v1 , 10.7546/nntdm.2025.31.2.299-304 , 10.14293/pr2199.001078.v2

On An Inequality about Euler’s totient function

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Abstract

In this paper, we show that when\(N_k\) is a primorial and \(\varphi(N_k)\)is Euler’s totient function, the inequality \(\varphi(N_k) < \frac{N_k}{e^{\gamma}\log{\log{N_k}}}\) holds for all sufficiently large k.

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