1680

Number
$1680$ (one thousand, six hundred and eighty) is:


 * $2^4 \times 3 \times 5 \times 7$


 * The $17$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$:
 * $\map \tau {1680} = 40$


 * The $17$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$:
 * $\dfrac {\map \sigma {1680} } {1680} = \dfrac {5952} {1680} \approx 3 \cdotp 543$


 * The $24$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$, $1408$, $1541$:
 * $1680 = \displaystyle \sum_{k \mathop = 1}^{24} \paren {6 k - 5} = 24 \paren {3 \times 24 - 2}$