2006/01/01 by Keith Briggs · 6 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Algebraic Geometry and Number Theory
paper · doi:10.1080/10586458.2006.10128957
openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this note I describe a computational study of the successive maxima of the relative sum-of-divisors function ρ(n) := σ(n)/n. These maxima occur at superabundant and colossally abundant numbers, and I also study the density of these numbers. The values are compared with the known maximal order eã log log (n); theorems of Robin and Lagarias relate these data to a condition equivalent to the Riemann hypothesis. It is thus interesting to see how close these conditions come to being violated.