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On the Sum of Reciprocals of Amicable Numbers
-
Jonathan Bayless
and
Dominic Klyve
Published/Copyright:
June 4, 2011
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.
Received: 2010-02-01
Revised: 2010-09-24
Accepted: 2010-12-26
Published Online: 2011-06-04
Published in Print: 2011-June
© de Gruyter 2011
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Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
