630

Number
$630$ (six hundred and thirty) is:


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


 * The $18$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$, $231$, $276$, $325$, $378$, $435$, $496$, $561$:
 * $630 = \ds \sum_{k \mathop = 1}^{18} \paren {4 k - 3} = 18 \paren {2 \times 18 - 1}$


 * The $20$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$, $78$, $105$, $140$, $168$, $190$, $210$, $248$, $264$, $357$, $420$, $570$, $616$ with the property that $\map \tau n \divides \map \phi n \divides \map \sigma n$:
 * $\map \tau {630} = 24$, $\map \phi {630} = 144$, $\map \sigma {630} = 1872$


 * The $35$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $325$, $351$, $378$, $406$, $435$, $465$, $496$, $528$, $561$, $595$:
 * $630 = \ds \sum_{k \mathop = 1}^{35} k = \dfrac {35 \times \paren {35 + 1} } 2$


 * The $39$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$, $360$, $420$, $480$, $504$, $600$:
 * $\map \sigma {630} = 1872$