8640

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Number

$8640$ (eight thousand, six hundred and forty) is:

$2^6 \times 3^3 \times 5$

The $54$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $5985$, $6256$, $6533$, $6816$, $7105$, $7400$, $7701$, $8008$, $8321$:

$8640 = \ds \sum_{k \mathop = 1}^{54} \paren {6 k - 5} = 54 \paren {3 \times 54 - 2}$

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