For a positive integer $n$, let $\sigma (n)$ denote the sum of the positive divisors of $n$. We call $n$ a near-perfect number if $\sigma (n) = 2n + d$ where $d$ is a proper divisor of $n$. We show that the only odd near-perfect number with four distinct prime divisors is $3^4\cdot 7^2\cdot 11^2\cdot 19^2$.
Keywords:
positive integer sigma denote sum positive divisors call near perfect number sigma where proper divisor nobreakspace only odd near perfect number distinct prime divisors cdot cdot cdot
Affiliations des auteurs :
Min Tang
1
;
Xiaoyan Ma
1
;
Min Feng
1
1
School of Mathematics and Computer Science Anhui Normal University Wuhu 241003, PR China
Min Tang; Xiaoyan Ma; Min Feng. On near-perfect numbers. Colloquium Mathematicum, Tome 144 (2016) no. 2, pp. 157-188. doi: 10.4064/cm6588-10-2015
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author = {Min Tang and Xiaoyan Ma and Min Feng},
title = {On near-perfect numbers},
journal = {Colloquium Mathematicum},
pages = {157--188},
year = {2016},
volume = {144},
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doi = {10.4064/cm6588-10-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6588-10-2015/}
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