A+ CATEGORY SCIENTIFIC UNIT

On near-perfect numbers

Volume 144 / 2016

Min Tang, Xiaoyan Ma, Min Feng Colloquium Mathematicum 144 (2016), 157-188 MSC: Primary 11A25. DOI: 10.4064/cm6588-10-2015 Published online: 3 March 2016

Abstract

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 $3^4\cdot 7^2\cdot 11^2\cdot 19^2$.

Authors

  • Min TangSchool of Mathematics and Computer Science
    Anhui Normal University
    Wuhu 241003, PR China
    e-mail
  • Xiaoyan MaSchool of Mathematics and Computer Science
    Anhui Normal University
    Wuhu 241003, PR China
  • Min FengSchool of Mathematics and Computer Science
    Anhui Normal University
    Wuhu 241003, PR China

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