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On the Sum of Reciprocals of Amicable Numbers

Jonathan Bayless / Dominic Klyve
Published Online: 2011-06-04 | DOI: https://doi.org/10.1515/integ.2011.025


Two numbers m and n are considered amicable if the sum of their proper divisors, s(n) and s(m), satisfy s(n) = m and s(m) = n. In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, P, is a constant. We obtain both a lower and an upper bound on the value of P.

Keywords.: Amicable Numbers; Explicit Bounds; Brun's Constant; Pomerance's Constant

About the article

Received: 2010-02-01

Revised: 2010-09-24

Accepted: 2010-12-26

Published Online: 2011-06-04

Published in Print: 2011-06-01

Citation Information: Integers, Volume 11, Issue 3, Pages 315–332, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.025.

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