420
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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 $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
- $\map {\sigma_0} {420} = 24$, $\map \phi {420} = 96$, $\map {\sigma_1} {420} = 1344$
- The $34$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$, $360$:
- $\map {\sigma_1} {420} = 1344$