Even harmonic numbers
by
Ronald M. Sorli
Dept of Mathematics, University of Technology, Sydney

Harmonic numbers were introduced by Ore in 1948. They are related to perfect and multiperfect numbers. No odd harmonic numbers have been found. A proof that none exist would constitute a proof that no odd perfect numbers exist (a long-standing unsolved problem).

While even harmonic numbers are plentiful, finding all of them below some limit is still a challenge. Most of them can be generated from a relatively small set of so called harmonic seeds using two simple rules.

An analysis of known harmonic numbers suggest two interesting properties of such numbers (a) every harmonic number has a unique harmonic seed and (b) only a finite number of harmonic numbers have the same harmonic seed.

This talk looks at these conjectures in the light of recent extended computational studies.

Date received: September 29, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caek-41.