Definition:Highly Composite Number

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

Then $n$ is highly composite :
 * $\forall m \in \Z_{>0}, m < n: \tau \left({m}\right) < \tau \left({n}\right)$

where $\sigma \left({n}\right)$ is the $\tau$ function of $n$.

That is, $n$ has a larger number of divisors than any smaller positive integer.

Also known as
Some sources use the term highly abundant number, but uses that term for a different concept.