4200

Number
$4200$ (four thousand two hundred) is:


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


 * The $20$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$, $405$, $550$, $726$, $936$, $1183$, $1470$, $1800$, $2176$, $2601$, $3078$, $3610$:
 * $4200 = \displaystyle \sum_{k \mathop = 1}^{20} \dfrac {k \paren {3 k - 1} } 2 = \dfrac {20^2 \paren {20 + 1} } 2$