Definition:Superabundant Number

Definition
Let $n \in \Z_{>0}$ be a positive integer.

Then $n$ is superabundant :
 * $\forall m \in \Z_{>0}, m < n: \dfrac {\map {\sigma_1} m} m < \dfrac {\map {\sigma_1} n} n$

where $\sigma_1$ denotes the divisor sum function.

That is, $n$ has a higher abundancy index than any smaller positive integer.