# 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 smallest EPORN:
$2520 = 210 \times 012 = 120 \times 021$

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

The $18$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:
$\map {\sigma_0} {2520} = 48$

The $18$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$:
$\dfrac {\map {\sigma_1} {2520} } {2520} = \dfrac {9360} {2520} \approx 3 \cdotp 714$

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

### Arithmetic Functions on $2520$

 $\ds \map {\sigma_0} { 2520 }$ $=$ $\ds 48$ $\sigma_0$ of $2520$ $\ds \map {\sigma_1} { 2520 }$ $=$ $\ds 9360$ $\sigma_1$ of $2520$