81 (number)

← 80 81 82 →
← 80 81 82 83 84 85 86 87 88 89 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	eighty-one
Ordinal	81st (eighty-first)
Factorization	34
Divisors	1, 3, 9, 27, 81
Greek numeral	ΠΑ´
Roman numeral	LXXXI, lxxxi
Binary	10100012
Ternary	100003
Senary	2136
Octal	1218
Duodecimal	6912
Hexadecimal	5116

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; 3 ⁴.
• 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. ^[1]
• a heptagonal number. ^[2]
• an icosioctagonal number. ^[3]
• a centered octagonal number. ^[4]
• a tribonacci number. ^[5]
• an open meandric number. ^[6]
• the ninth member of the Mian-Chowla sequence. ^[7]
• 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 0.012345679 recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,

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

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. ^[8]
• 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. 81 is the second most points scored in a game, behind Wilt Chamberlain's 100.

References

1. Sloane, N. J. A. (ed.). "SequenceA082897(Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA000566(Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA161935(28-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA016754(Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA000073(Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA005316(Meandric numbers: number of ways a river can cross a road n times.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA005282(Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Kovalevski, Serge F. (November 28, 2013), "Despite Outlaw Image, Hells Angels Sue Often", The New York Times .