Ramanujan’s Theorem and Highest Abundant Numbers

Authors

Oleg R. Musin, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

4-2020

Abstract

In 1915, Ramanujan proved asymptotic inequalities for the sum of divisors function, assuming the Riemann hypothesis (RH). We consider a strong version of Ramanujan’s theorem and define highest abundant numbers that are extreme with respect to the Ramanujan and Robin inequalities. Properties of these numbers are very different depending on whether the RH is true or false.

Recommended Citation

Musin, Oleg R. "Ramanujan’s theorem and highest abundant numbers." Arnold Mathematical Journal 6, no. 1 (2020): 119-130. https://doi.org/10.1007/s40598-020-00136-w

Publication Title

Arnold Mathematical Journal

DOI

10.1007/s40598-020-00136-w