Geodesic
On near-perfect and deficient-perfect numbers
Min Tang 1   ; Xiao-Zhi Ren 2   ; Meng Li 1
1 Department of Mathematics Anhui Normal University Wuhu 241003, China
2 School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China
Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 221-226 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 $n$. Let $d$ be a proper divisor of $n$. We call $n$ a near-perfect number if $\sigma (n) = 2n + d$, and a deficient-perfect number if $\sigma (n) = 2n - d$. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
DOI : 10.4064/cm133-2-8
Keywords: positive integer sigma denote sum positive divisors proper divisor call near perfect number sigma deficient perfect number sigma there odd near perfect number three distinct prime divisors determine deficient perfect numbers distinct prime factors

Min Tang  1   ; Xiao-Zhi Ren  2   ; Meng Li  1

1 Department of Mathematics Anhui Normal University Wuhu 241003, China
2 School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China 
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Min Tang; Xiao-Zhi Ren; Meng Li. On near-perfect and deficient-perfect numbers. Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 221-226. doi: 10.4064/cm133-2-8

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