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ON DEFICIENT-PERFECT NUMBERS

Part of: Elementary number theory

Published online by Cambridge University Press:  23 May 2014

MIN TANG  and
MIN FENG
MIN TANG*
Affiliation:
School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, PR China email [email protected]
MIN FENG
Affiliation:
School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, PR China
*
✉[email protected]
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Abstract

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For a positive integer $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$, 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 there are no odd deficient-perfect numbers with three distinct prime divisors.

Keywords

almost perfect numberdeficient-perfect numbernear-perfect number

MSC classification

Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 186 - 194
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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