\begin{definition}[Definition:Highly Composite Number]
Let $n \in \Z_{>0}$ be a positive integer.
Then $n$ is '''highly composite''' {{iff}}:
:$\forall m \in \Z_{>0}, m < n: \map \tau m < \map \tau n$
where $\map \tau n$ is the divisor counting (tau) function of $n$.
That is, {{iff}} $n$ has a larger number of divisors than any smaller positive integer.
\end{definition}