On the Sum of Reciprocals of Amicable Numbers

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 $P$.

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