216

Number
$216$ (two hundred and sixteen) is:
 * $2^3 \times 3^3$


 * The $6$th cube number after $1, 8, 27, 64, 125$:
 * $216 = 6 \times 6 \times 6$


 * The $24$th powerful number after $1, 4, 8, 9, 16, 25, \ldots, 108, 121, 125, 128, 144, 169, 196, 200$


 * The $28$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 210$:
 * $\sigma \left({216}\right) = 600$


 * The $10$th inconsummate number after $62, 63, 65, 75, 84, 95, 161, 173, 195$:
 * $\nexists n \in \Z_{>0}: n = 216 \times s_{10} \left({n}\right)$


 * The $13$th untouchable number after $2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210$.


 * The $1$st element of the $2$nd set of $4$ positive integers which form an arithmetic progression which all have the same Euler $\phi$ value:
 * $\phi \left({216}\right) = \phi \left({222}\right) = \phi \left({228}\right) = \phi \left({234}\right) = 72$


 * The $7$th positive integer after $64, 96, 128, 144, 160, 192$ with $6$ or more prime factors:
 * $216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3$


 * The $12$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
 * $73, 91, 95, 111, 117, 135, 146, 148, 152, 182, 190, 216, 222, 228, 234, 252, 270$


 * The $1$st cube which can be expressed as the sum of $3$ positive cubes:
 * $216 = 3^3 + 4^3 + 5^3$


 * The $42$nd positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.

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