# 2520

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## Number

$2520$ (two thousand, five hundred and twenty) is:

$2^3 \times 3^2 \times 5 \times 7$
and so is the lowest common multiple of all the digits from $1$ to $9$

The $6$th and last special highly composite number after $1$, $2$, $6$, $12$, $60$

The $18$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:
$\map \tau {2520} = 48$

The $18$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:
$\dfrac {\map \sigma {2520} } {2520} = \dfrac {9360} {2520} \approx 3 \cdotp 714$

The sum of $4$ of its divisors in $6$ different ways:
 $\displaystyle \qquad \ \$ $\displaystyle 2520$ $=$ $\displaystyle 1260 + 630 + 504 + 126$ $\displaystyle$ $=$ $\displaystyle 1260 + 630 + 421 + 210$ $\displaystyle$ $=$ $\displaystyle 1260 + 840 + 360 + 60$ $\displaystyle$ $=$ $\displaystyle 1260 + 840 + 315 + 105$ $\displaystyle$ $=$ $\displaystyle 1260 + 840 + 280 + 140$ $\displaystyle$ $=$ $\displaystyle 1260 + 840 + 252 + 168$

### Arithmetic Functions on $2520$

 $\displaystyle \map \tau { 2520 }$ $=$ $\displaystyle 48$ $\tau$ of $2520$ $\displaystyle \map \sigma { 2520 }$ $=$ $\displaystyle 9360$ $\sigma$ of $2520$