405

Number
$405$ (four hundred and five) is:


 * $3^4 \times 5$


 * The $9$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$:
 * $405 = 1 + 5 + 12 + 22 + 35 + 51 + 70 + 92 + 117 = \dfrac {9^2 \paren {9 + 1} } 2$