Special Highly Composite Number/Examples/2

Example of Special Highly Composite Number
$2$ is a special highly composite number, being a highly composite number which is a divisor of all larger highly composite numbers.

Proof
We have that $2$ is highly composite.

Let $n > 2$ be a highly composite number.

From Prime Decomposition of Highly Composite Number, the multiplicity of $2$ in $n$ is at least as high as the multiplicity of any other prime $p$ in $n$.

Thus if $p \mathop \backslash n$ it follows that $2 \mathop \backslash n$.

Thus, by definition, $2$ is a special highly composite number.