+413 A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. What is the smallest possible value of $n?$
+135 There are 2 cases:
n=p81 or n=p21p22
But wait! 8=23, so the second possibility won't work since it must not be divisible by a power of 2 greater than 4. Therefore, the smallest (and only) ice number with exactly 9 divisors is 28=256
