Geodesic
On near-perfect numbers
Min Tang 1   ; Xiaoyan Ma 1   ; Min Feng 1
1 School of Mathematics and Computer Science Anhui Normal University Wuhu 241003, PR China
Colloquium Mathematicum, Tome 144 (2016) no. 2, pp. 157-188 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $3^4\cdot 7^2\cdot 11^2\cdot 19^2$.
DOI : 10.4064/cm6588-10-2015
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

Min Tang  1   ; Xiaoyan Ma  1   ; Min Feng  1

1 School of Mathematics and Computer Science Anhui Normal University Wuhu 241003, PR China 
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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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