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ON DEFICIENT-PERFECT NUMBERS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 90 / Issue 2 / October 2014
- Published online by Cambridge University Press:
- 23 May 2014, pp. 186-194
- Print publication:
- October 2014
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- Article
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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.
