Highly Composite Number/Examples/2

Example of Highly Composite Number

$2$ is a highly composite number, being the smallest positive integer with $2$ divisors or more.

Proof

From $\sigma_0$ of $2$:

$\map {\sigma_0} 2 = 2$

From $\sigma_0$ of $1$:

$\map {\sigma_0} 1 = 1$

That is, the only positive integer smaller than $2$ has a smaller number of divisors.

Thus, despite not actually being composite, $2$ is a highly composite number.

$\blacksquare$