# 6441

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## Number

$6441$ (six thousand, four hundred and forty-one) is:

$3 \times 19 \times 113$

The $57$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $4005$, $4186$, $4371$, $4560$, $4950$, $5151$, $5356$, $5565$, $5778$, $5995$, $6216$:
$6441 = \ds \sum_{k \mathop = 1}^{57} \paren {4 k - 3} = 57 \paren {2 \times 57 - 1}$

The $113$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $5253$, $5356$, $5460$, $5565$, $5671$, $5778$, $5886$, $5995$, $6105$, $6216$, $6328$:
$6441 = \ds \sum_{k \mathop = 1}^{113} k = \dfrac {113 \times \paren {113 + 1} } 2$