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The 4-Nicol Numbers Having
Five Different Prime Divisors Qiao-Xiao Jin and Min Tang¹
Department of Mathematics
Anhui Normal University
Wuhu 241000
P. R. China
mailto:tangmin@mail.ahnu.edu.cntangmin@mail.ahnu.edu.cn

Abstract:

A positive integer $n$ is called a Nicol number if $n\mid \varphi(n)+\sigma(n)$, and a t-Nicol number if $\varphi(n)+\sigma(n)=tn$. In this paper, we show that if $n$ is a 4-Nicol number which has five different prime divisors, then $n=2^{\alpha_{1}}\cdot 3\cdot 5^{\alpha_{3}}\cdot p^{\alpha_{4}}\cdot q^{\alpha_{5}}$, or $n=2^{\alpha_{1}}\cdot 3\cdot 7^{\alpha_{3}}\cdot p^{\alpha_{4}}\cdot q^{\alpha_{5}}$ with $p\leq 29$.