40,755

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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:

$40 \, 755 = \ds \sum_{k \mathop = 1}^{143} \paren {4 k - 3} = 143 \paren {2 \times 143 - 1}$

The $165$th pentagonal number:

$40 \, 755 = \ds \sum_{k \mathop = 1}^{165} \paren {3 k - 2} = \dfrac {165 \paren {3 \times 165 - 1} } 2$

The $285$th triangular number:

$40 \, 755 = \ds \sum_{k \mathop = 1}^{285} k = \dfrac {285 \times \paren {285 + 1} } 2$

The $329$th generalized pentagonal number:

$40 \, 755 = \ds \sum_{k \mathop = 1}^{165} \paren {3 k - 2} = \dfrac {165 \paren {3 \times 165 - 1} } 2$

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $40,755$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $40,755$