Families of Values of the Excedent Function σ(n)−2n
Department or Administrative Unit
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.
Dean, R. et al. (2015). Families of values of the excedent function σ(n)−2n. Missouri Journal of Mathematical Sciences 27(1), 37-46. http://projecteuclid.org/euclid.mjms/1449161366
Missouri Journal of Mathematical Sciences
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