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