576

Number
$576$ (five hundred and seventy-six) is:
 * $2^6 \times 3^2$


 * The $9$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$ to be the $\sigma$ (sigma) value of some (strictly) positive integer:
 * $576 = \map \sigma {210} = \map \sigma {282} = \map \sigma {310} = \map \sigma {345} = \map \sigma {357} = \map \sigma {382} = \map \sigma {385}$


 * The $11$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$, $432$, $448$, $480$, $512$ with $7$ or more prime factors:
 * $512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \paren {\times \, 3}$


 * The $24$th square number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $361$, $392$, $400$, $432$, $441$, $484$, $529$:
 * $576 = 24 \times 24$


 * The $25$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $346$, $355$, $378$, $382$, $391$, $438$, $454$, $483$, $517$, $526$, $535$, $562$:
 * $5 + 7 + 6 = 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = 18$


 * The $41$st powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $400$, $432$, $441$, $484$, $500$, $512$, $529$:
 * $576 = 2^6 \times 3^2$


 * The $47$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $472$, $474$, $498$, $516$, $518$, $520$, $530$, $540$, $552$, $556$, $562$