630

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


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


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


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


 * 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 $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma\left({n}\right)$:
 * $\tau \left({630}\right) = 24$, $\phi \left({630}\right) = 144$, $\sigma \left({630}\right) = 1872$