On odd deficient-perfect numbers with four distinct prime divisors
Abstract
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 $3^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2019
- DOI:
- 10.48550/arXiv.1908.04932
- arXiv:
- arXiv:1908.04932
- Bibcode:
- 2019arXiv190804932S
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 47 pages