Eighty-one is the square of 9 and the fourth power of 3. Like all powers of three, 81 is a perfect totient number. It is a heptagonal number and a centered octagonal number. It is also a tribonacci number, and an open meandric number. 81 is the ninth member of the Mian-Chowla sequence.
The inverse of 81 is 0.012345679 recurring, tantalisingly close to being a repeating set of all the digits 0-9 successively. The full sequence is reserved for the significantly more cumbersome fraction 13,717,421/1,111,111,111.
I love the internets.