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November 2015 Families of Values of the Excedent Function $\sigma (n) - 2n$
Raven Dean, Rick Erdman, Dominic Klyve, Emily Lycette, Melissa Pidde, Derek Wheel
Missouri J. Math. Sci. 27(1): 37-46 (November 2015). DOI: 10.35834/mjms/1449161366

Abstract

The excedent function, $e(n) := \sigma(n) - 2n$, 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.

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Raven Dean. Rick Erdman. Dominic Klyve. Emily Lycette. Melissa Pidde. Derek Wheel. "Families of Values of the Excedent Function $\sigma (n) - 2n$." Missouri J. Math. Sci. 27 (1) 37 - 46, November 2015. https://doi.org/10.35834/mjms/1449161366

Information

Published: November 2015
First available in Project Euclid: 3 December 2015

zbMATH: 06555649
MathSciNet: MR3431114
Digital Object Identifier: 10.35834/mjms/1449161366

Subjects:
Primary: 11A25

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

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Vol.27 • No. 1 • November 2015
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