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arXiv · 1101.0259

On the Sum of Reciprocals of Amicable Numbers

Jonathan Bayless·Dominic Klyve
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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 $P$.

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Jonathan Bayless, Dominic Klyve. 2010-12-31. On the Sum of Reciprocals of Amicable Numbers. https://arxiv.org/abs/1101.0259

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