324

Number
$324$ (three hundred and twenty-four) is:


 * $2^2 \times 3^4$


 * The $7$th square number after $1$, $4$, $36$, $121$, $144$, $256$ to be the $\sigma$ (sigma) value of some (strictly) positive integer:
 * $324 = \map \sigma {170} = \map \sigma {214} = \map \sigma {265}$


 * The $9$th positive integer after $200$, $202$, $204$, $205$, $206$, $208$, $320$, $322$ that cannot be made into a prime number by changing just $1$ digit


 * The $13$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
 * $3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$


 * The $13$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$, $240$, $256$, $288$, $320$ with $6$ or more prime factors:
 * $324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3$


 * The $16$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $\ldots$


 * The $18$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$, $144$, $169$, $196$, $225$, $256$, $289$:
 * $324 = 18 \times 18$


 * The $26$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $262$, $268$, $276$, $288$, $290$, $292$, $304$, $306$, $322$


 * The $30$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $144$, $169$, $196$, $200$, $216$, $225$, $243$, $256$, $288$, $289$