1540

Number
$1540$ (one thousand, five hundred and forty) is:
 * $2^2 \times 5 \times 7 \times 11$


 * The $55$th triangular number:
 * $1540 = \displaystyle \sum_{k \mathop = 1}^{55} k = \dfrac {55 \times \left({55 + 1}\right)} 2$


 * The $28$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$:
 * $1540 = \displaystyle \sum_{k \mathop = 1}^{28} \left({4 k - 3}\right) = 28 \left({2 \times 28 - 1}\right)$


 * The $20$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$, $286$, $364$, $455$, $560$, $680$, $816$, $969$, $1140$, $1330$:
 * $1540 = \displaystyle \sum_{k \mathop = 1}^{20} \frac {k \left({k + 1}\right)} 2 = \dfrac {20 \left({20 + 1}\right) \left({20 + 2}\right)} 6$


 * The $4$th after $1$, $10$, $120$ of the $5$ tetrahedral numbers which are also triangular.