360

Number
$360$ (three hundred and sixty) is:
 * $2^3 \times 3^2 \times 5$


 * The $1$st number whose ratio to aliquot sum is $4 : 9$:
 * $\dfrac {\map {\sigma_1} {360} - 360} {360} = \dfrac 9 4$
 * where $\sigma_1$ denotes the divisor sum function.


 * The $13$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$:
 * $\map {\sigma_0} {360} = 24$


 * The $13$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$:
 * $\dfrac {\map {\sigma_1} {360} } {360} = \dfrac {1170} {360} = 3 \cdotp 25$


 * The $16$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$, $240$, $256$, $288$, $320$, $324$, $336$, $352$ with $6$ or more prime factors:
 * $360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5$


 * The $33$rd highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$:
 * $\map {\sigma_1} {360} = 1170$


 * The divisor sum of $120$:
 * $\map {\sigma_1} {120} = 360 = 3 \times 120$

Also see

 * Ratio of 360 to Aliquot Sum