vix.ing · top · new · best · stats

On the Sum of Reciprocals of Amicable Numbers

2010/12/31 by Jonathan Bayless, Bayless, Jonathan, Dominic Klyve +1
Mathematics · #11A99 #11Y60 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A99 #msc:11Y60

paper · pdf · doi:10.48550/arxiv.1101.0259

18 pages. Paper version to appear in Integers; work first presented at Integers Conference 2009

arxiv created 2010/12/31 · arxiv updated 2011/01/04

Abstract

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.

Related