# 7560

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## Number

$7560$ (seven thousand, five hundred and sixty) is:

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

The $1$st highly composite number which is not also superabundant:
$\dfrac {\map \sigma {7560} } {7560} = \dfrac {28 \, 800} {7560} \approx 3 \cdotp 810$, but $\dfrac {\map \sigma {5040} } {5040} = \dfrac {19 \, 344} {5040} \approx 3 \cdotp 838$, which is greater

The $20$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$, $840$, $1260$, $1680$, $2520$, $5040$:
$\map \tau {7560} = 64$

### Arithmetic Functions on $7560$

 $\ds \map \tau { 7560 }$ $=$ $\ds 64$ $\tau$ of $7560$ $\ds \map \sigma { 7560 }$ $=$ $\ds 28 \, 800$ $\sigma$ of $7560$