Missouri Journal of Mathematical Sciences
- Missouri J. Math. Sci.
- Volume 27, Issue 1 (2015), 37-46.
Families of Values of the Excedent Function $\sigma (n) - 2n$
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.
Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 37-46.
First available in Project Euclid: 3 December 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Dean, Raven; Erdman, Rick; Klyve, Dominic; Lycette, Emily; Pidde, Melissa; Wheel, Derek. Families of Values of the Excedent Function $\sigma (n) - 2n$. Missouri J. Math. Sci. 27 (2015), no. 1, 37--46. doi:10.35834/mjms/1449161366. https://projecteuclid.org/euclid.mjms/1449161366