Category:Highly Abundant Numbers

This category contains results about Highly Abundant Numbers.
Definitions specific to this category can be found in Definitions/Highly Abundant Numbers.

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

Then $n$ is highly abundant if and only if:

$\forall m \in \Z_{>0}, m < n: \map {\sigma_1} m < \map {\sigma_1} n$

where $\sigma_1$ denotes the divisor sum function of $n$.