A colossally abundant number is a positive integer n for which there is a positive exponent ϵ such that (σ(n))/n^(1 + ϵ)>=(σ(k))/k^(1 + ϵ) for all k>1. All colossally abundant numbers are superabundant numbers. The first few are 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800, 160626866400, ... (OEIS A004490). The following table lists the colossally abundant numbers up to 10^18, as given by Alaoglu and Erdős.

abundant number | superabundant number | superior highly composite number