9

The natural number $9$ has the following properties:
 * $9$ is the successor of $8$.
 * The prime factorization of $9$ is $9 = 3^2$.
 * $9$ is a perfect square.
 * The pair $(8,9)$ is the only pair of numbers $(x,y)$ which satisfies:
 * $x$ and $y$ are consecutive nonzero natural numbers.
 * There exist natural numbers $a,e$, such that $e > 1$ and $x = a^e$.
 * There exist natural numbers $b,f$, such that $f > 1$ and $y = b^f$.
 * $9$ is the number of sides of a nonagon.