On near-perfect numbers with two distinct prime factors (Q2872022)
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scientific article; zbMATH DE number 6245030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On near-perfect numbers with two distinct prime factors |
scientific article; zbMATH DE number 6245030 |
Statements
14 January 2014
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perfect number
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sum-of-divisors function
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near-perfect number
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Mersenne prime
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pseudoperfect number
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semiperfect number
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On near-perfect numbers with two distinct prime factors (English)
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A positive integer is called near-perfect if it is the sum of all but one of its proper divisors. \textit{P. Pollack} and \textit{V. Shevelev} [J. Number Theory 132, No. 12, 3037--3046 (2012; Zbl 1272.11013)] constructed three types of near-perfect numbers. The present authors show that all near-perfect numbers (except for 40) with two distinct prime factors are of these types. Two of these types are related with Mersenne primes. Near-perfect numbers are special cases of pseudoperfect or semiperfect numbers.
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