Missouri Journal of Mathematical Sciences

Families of Values of the Excedent Function $\sigma (n) - 2n$

Raven Dean, Rick Erdman, Dominic Klyve, Emily Lycette, Melissa Pidde, and Derek Wheel

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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.

Article information

Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 37-46.

First available in Project Euclid: 3 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A25: Arithmetic functions; related numbers; inversion formulas

sum-of-divisors almost-perfect numbers aliquot parts Mersenne primes


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. https://projecteuclid.org/euclid.mjms/1449161366

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