Category:Definitions/Highly Abundant Numbers

This category contains definitions related to Highly Abundant Numbers.
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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 $n$.