408

Number
$408$ (four hundred and eight) is:


 * $2^3 \times 3 \times 17$


 * The $12$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$, $176$, $225$, $280$, $341$:
 * $408 = \ds \sum_{k \mathop = 1}^{12} \paren {6 k - 5} = 12 \paren {3 \times 12 - 2}$


 * The $32$nd untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $324$, $326$, $336$, $342$, $372$, $406$