420

Number
$420$ (four hundred and twenty) is:


 * $2^2 \times 3 \times 5 \times 7$


 * The $17$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$, $78$, $105$, $140$, $168$, $190$, $210$, $248$, $264$, $357$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map \sigma n$:
 * $\map {\sigma_0} {420} = 24$, $\map \phi {420} = 96$, $\map \sigma {420} = 1344$


 * The $34$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$, $360$:
 * $\map \sigma {420} = 1344$