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arXiv · 2206.10355

On a conjecture of Deaconescu

Elchin Hasanalizade
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Abstract

In 2000 Deaconescu raised a question whether there exists a composite $n$ for which $S_2(n)|ϕ(n)-1$, where $ϕ(n)$ is Euler's function and $S_2(n)$ 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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Elchin Hasanalizade. 2022-06-14. On a conjecture of Deaconescu. https://arxiv.org/abs/2206.10355

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