40,755

Number
$40 \, 755$ (forty thousand, seven hundred and fifty-five) is:


 * $3 \times 5 \times 11 \times 13 \times 19$


 * The $2$nd integer after $1$ to be both pentagonal and hexagonal


 * The $3$rd integer after $1$, $210$ to be both pentagonal and triangular


 * The $143$rd hexagonal number:
 * $40 \, 755 = \displaystyle \sum_{k \mathop = 1}^{143} \paren {4 k - 3} = 143 \paren {2 \times 143 - 1}$


 * The $165$th pentagonal number:
 * $40 \, 755 = \displaystyle \sum_{k \mathop = 1}^{165} \paren {3 k - 2} = \dfrac {165 \paren {3 \times 165 - 1} } 2$


 * The $285$th triangular number:
 * $40 \, 755 = \displaystyle \sum_{k \mathop = 1}^{285} k = \dfrac {285 \times \paren {285 + 1} } 2$


 * The $329$th generalized pentagonal number:
 * $40 \, 755 = \displaystyle \sum_{k \mathop = 1}^{165} \paren {3 k - 2} = \dfrac {165 \paren {3 \times 165 - 1} } 2$

Also see