# 8385

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## Number

$8385$ (eight thousand, three hundred and eighty-five) is:

$3 \times 5 \times 13 \times 43$

The $65$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $6903$, $7140$, $7381$, $7626$, $7875$, $8128$:
$8385 = \ds \sum_{k \mathop = 1}^{65} \paren {4 k - 3} = 65 \paren {2 \times 65 - 1}$

The $129$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $7503$, $7626$, $7750$, $7875$, $8001$, $8128$, $8256$:
$8385 = \ds \sum_{k \mathop = 1}^{129} k = \dfrac {129 \times \paren {129 + 1} } 2$