While highly composite numbers relate to the number of divisors, an even closer fit to the Robin inequality are the somewhat similar superabundant and colossall

While highly composite numbers relate to the number of divisors, an even closer fit to the Robin inequality are the somewhat similar superabundant and colossally abundant numbers, which relate to the sum of divisors instead. https://en.wikipedia.org/wiki/Superabundant_number https://en.wikipedia.org/wiki/Superabundant_number In fact if counterexamples to the inequality exist, the smallest such counterexample must be a superabundant number. This is a nice, accessible paper about searching for counterexamples to the inequality by generating superabundant and colossally abundant numbers: https://projecteuclid.org/euclid.em/1175789744 https://projecteuclid.org/euclid.em/1175789744