2380
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Number
$2380$ (two thousand, three hundred and eighty) is:
- $2^2 \times 5 \times 7 \times 17$
- The $14$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$, $715$, $1001$, $1365$, $1820$:
- $2380 = \ds \sum_{k \mathop = 1}^{14} \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {14 \paren {14 + 1} \paren {14 + 2} \paren {14 + 3} } {24}$
- The $40$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $1820$, $1926$, $2035$, $2147$, $2262$:
- $2380 = \ds\sum_{k \mathop = 1}^{40} \paren {3 k - 2} = \dfrac {40 \paren {3 \times 40 - 1} } 2$
- The $79$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1617$, $1650$, $1717$, $1751$, $1820$, $1855$, $1926$, $1962$, $2072$, $2147$, $2185$, $2262$, $2301$:
- $2380 = \ds \sum_{k \mathop = 1}^{40} \paren {3 k - 2} = \dfrac {40 \paren {3 \times 40 - 1} } 2$