Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.8

Egyptian Fractions with Denominators from Sequences Closed Under Doubling

David Eppstein
Department of Computer Science
University of California, Irvine
Irvine, CA 92697


Resolving a conjecture of Zhi-Wei Sun, we prove that every rational number can be represented as a sum of distinct unit fractions whose denominators are practical numbers. The same method applies to allowed denominators that are closed under multiplication by two and include a multiple of every positive integer, including the odious numbers, evil numbers, Hardy-Ramanujan numbers, Jordan-Pólya numbers, and fibbinary numbers.

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(Concerned with sequences A000069 A000695 A001013 A001969 A003714 A005153 A025487 A116882 A126684 A178757 A300867.)

Received July 19 2021; revised version received September 23 2021. Published in Journal of Integer Sequences, September 24 2021.

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