40,755

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


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


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


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


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


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


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


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

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