On a conjecture of Deaconescu

2022/06/14 by Elchin Hasanalizade, Hasanalizade, Elchin
Mathematics · #Advanced Mathematical Theories #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT #msc:11A25

paper · pdf · doi:10.48550/arxiv.2206.10355

4 pages

Abstract

In 2000 Deaconescu raised a question whether there exists a composite n for which S₂(n)|ϕ(n)-1, where ϕ(n) is Euler's function and S₂(n) is Schemmel's totient function. In this paper we prove that any such n is odd, squarefree and has at least seven distinct prime factors. We also prove that any such n with exactly K distinct prime divisors is necessarily less than 2^2^K+1.

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• On Sparsely Schemmel Totient Numbers
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