On odd deficient-perfect numbers with four distinct prime divisors

For a positive integer \(n\), let \(\sigma(n)\) denote the sum of the positive divisors of \(n\). Let \(d\) be a proper divisor of \(n\). We call \(n\) a deficient-perfect number if \(\sigma(n)=2n-d\). In this paper, we show that the only odd deficient-perfect number with four distinct prime divisor...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Authors: Cui-Fang, Sun, Zhao-Cheng, He
Format: Article
Language:English
Subjects:
Numbers
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Summary:For a positive integer \(n\), let \(\sigma(n)\) denote the sum of the positive divisors of \(n\). Let \(d\) be a proper divisor of \(n\). We call \(n\) a deficient-perfect number if \(\sigma(n)=2n-d\). In this paper, we show that the only odd deficient-perfect number with four distinct prime divisors is \(3^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\).
ISSN:2331-8422