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Publication Date:
24 01 2012
DOI:
10.1515/integ.2011.090

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Integers

Editor-in-Chief: Nathanson, Melvyn B. / Nešetril, Jaroslav / Pomerance, Carl

6 Issues per year

Mathematical Citation Quotient 2010: 0.20

Aliquot Cycles of Repdigits

1 / 2

1Instituto de Matemáticas, Universidad Nacional Autonoma de México, Morelia, Michoacán, Mexico

2Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Citation Information: Integers. Volume 12, Issue 1, Pages 129–140, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: 10.1515/integ.2011.090, January 2012

Publication History:

Received: 17/01/2011;
Revised: 28/06/2011;
Accepted: 22/08/2011;
Published Online: 27/02/2012

Abstract.

Here we show that the only aliquot cycle consisting only of rep-digits in base 10 is the cycle consisting of the perfect number 6. Generally, we show that if g is an even positive integer, then there are only finitely many aliquot cycles consisting entirely of repdigits in base g, which are, at least in principle, effectively computable.

Keywords.: Aliquot Cycles; Repdigits; Divisor Sum

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