288 (number)

288 is a pentagonal pyramidal number, is 4 superfactorial since 288 = 1!·2!·3!·4!

288 is an untouchable number, a Harshad number in base 10 and base 12, an Achilles number, a 3-smooth number and a self number.

Both 288 and 289 are powerful numbers.

288 is sum of the sequence of integers 1..4 to the second tetration (i.e. [math]\displaystyle{ 288=\sum_{k=1}^{4}{(k[4]2)} }[/math], where [math]\displaystyle{ a[n]b }[/math] is the hyperoperation) since 288 = 1 + 4 + 27 + 256 = 1¹ + 2² + 3³ + 4⁴.

288 is the number of labelled pointed rooted trees (vertebrates) with up to 4 nodes, the number of maximal directed Pseudoforests on up to 4 vertices, the number of Endofunctions for all sets with ≤ 4 points, and is two dozen sets of a dozen, thus being two gross and being 200 in base 12, often told as a pun in maths classes.

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