Families of Values of the Excedent Function σ(n)−2n

Department or Administrative Unit

Mathematics

Document Type

Article

Author Copyright

Copyright © 2015 Central Missouri State University, Department of Mathematics and Computer Science

Publication Date

2015

Journal

Missouri Journal of Mathematical Sciences

Abstract

The excedent function, e(n)=σ(n)−2n, measures the amount by which the sum of the divisors of an integer exceeds that integer. Despite having been in the mathematical consciousness for more than 2000 years, there are many unanswered questions concerning the function. Of particular importance to us is the question of explaining and classifying values in the image of e(n) — especially in understanding the "small" values. We look at extensive calculated data, and use them as inspiration for new results, generalizing theorems in the literature, to better understand a family of values in this image.

Comments

This article was originally published in Missouri Journal of Mathematical Sciences. The full-text article from the publisher can be found here.

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