On the Sum of Reciprocals of Amicable Numbers

Jonathan Bayless; Dominic Klyve

On the Sum of Reciprocals of Amicable Numbers

Number Theory 2011-01-04 v1

Authors: Jonathan Bayless , Dominic Klyve

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 $P$ .

Keywords

amicable numbers sum of reciprocals proper divisors number theory bounds

Cite

@article{arxiv.1101.0259,
  title  = {On the Sum of Reciprocals of Amicable Numbers},
  author = {Jonathan Bayless and Dominic Klyve},
  journal= {arXiv preprint arXiv:1101.0259},
  year   = {2011}
}

Comments

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

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