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ON NEAR-PERFECT NUMBERS WITH TWO DISTINCT PRIME FACTORS

Part of: Elementary number theory Sequences and sets

Published online by Cambridge University Press:  11 March 2013

XIAO-ZHI REN  and
YONG-GAO CHEN
XIAO-ZHI REN
Affiliation:
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, PR China
YONG-GAO CHEN*
Affiliation:
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, PR China
*
✉[email protected]
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Abstract

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Recently, Pollack and Shevelev [‘On perfect and near-perfect numbers’, J. Number Theory 132 (2012), 3037–3046] introduced the concept of near-perfect numbers. A positive integer $n$ is called near-perfect if it is the sum of all but one of its proper divisors. In this paper, we determine all near-perfect numbers with two distinct prime factors.

Keywords

perfect numbersum-of-divisors functionnear-perfect number

MSC classification

Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas 11B83: Special sequences and polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 520 - 524
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Crandall, R. and Pomerance, C., Prime Numbers: A Computational Perspective, 2nd edn (Springer, New York, 2005).Google Scholar
Pollack, P. and Shevelev, V., ‘On perfect and near-perfect numbers’, J. Number Theory 132 (2012), 3037–3046.CrossRefGoogle Scholar
Sloane, N. J., ‘The online encyclopedia of integer sequences’, available at http://oeis.org/.Google Scholar