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 $2520$


Also see



Sources