8 research outputs found
Finite connected components of the aliquot graph
Conditional on a strong form of the Goldbach conjecture, we determine all
finite connected components of the aliquot graph containing a number less than
, as well as those containing an amicable pair below or one of
the known perfect or sociable cycles below . Along the way we develop
a fast algorithm for computing the inverse image of an even number under the
sum-of-proper-divisors function.Comment: 10 pages, to appear in Mathematics of Computatio
Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton
Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions