81 (number)

Template:Infobox number 81 (eighty-one) is the natural number following 80 and preceding 82.

In mathematics

81 is:

• the square of 9 and the second fourth-power of a prime; 3⁴.
• with an aliquot sum of 40; within an aliquot sequence of three composite numbers (81,40,50,43,1,0) to the Prime in the 43-aliquot tree.
• a perfect totient number like all powers of three.
• a heptagonal number.
• an icosioctagonal number.
• a centered octagonal number.
• a tribonacci number.
• an open meandric number.
• the ninth member of the Mian-Chowla sequence.
• a palindromic number in bases 8 (121₈) and 26 (33₂₆).
• a Harshad number in bases 2, 3, 4, 7, 9, 10 and 13.
• one of three non-trivial numbers (the other two are 1458 and 1729) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number:

8 + 1 = 9

9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit).

The inverse of 81 is 0.Template:Overline recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,

$\frac{1}{{(b-1)}^2}=0.\overline{012\cdots (b-4)(b-3)(b-1)},$

omitting only the digit b−2.

In other fields

Eighty-one is also:

• The number of chapters in the Tao Te Ching, the foundational text of Taoism.
• The symbolic number of the Hells Angels Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.
• 81 (八一) is referenced in flags and symbols of the People's Liberation Army as it was founded on August 1 (8/1).
• The career high of points scored in a single game by Kobe Bryant on January 22, 2006 against the Toronto Raptors.