# 9180

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## Number

$9180$ (nine thousand, one hundred and eighty) is:

$2^2 \times 3^3 \times 5 \times 17$

The $68$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $6903$, $7140$, $7381$, $7626$, $7875$, $8128$, $8385$, $8646$, $8911$:
$9180 = \ds \sum_{k \mathop = 1}^{68} \paren {4 k - 3} = 68 \paren {2 \times 68 - 1}$

The $135$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $7503$, $7626$, $7750$, $7875$, $8001$, $8128$, $8256$, $8385$, $8515$, $8646$, $8778$, $8911$, $9045$:
$9180 = \ds \sum_{k \mathop = 1}^{135} k = \dfrac {135 \times \paren {135 + 1} } 2$