Category:Definitions/Highly Composite Numbers

This category contains definitions related to Highly Composite Numbers.
Related results can be found in Category:Highly Composite Numbers.

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

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

$\forall m \in \Z_{>0}, m < n: \map {\sigma_0} m < \map {\sigma_0} n$

where $\map {\sigma_0} n$ is the divisor count function of $n$.