81 (number)

Natural 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
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[edit]

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.[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).

Look up eighty-one in Wiktionary, the free dictionary.

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,

1 ( b − 1 ) 2 = 0. 012 ⋯ ( b − 4 ) ( b − 3 ) ( b − 1 ) ¯ , {\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 astronomy[edit]

* Messier object M81, a magnitude 8.5 spiral galaxy in the constellation Ursa Major, also known as Bode's Galaxy, and the first of what is known as the M81 Group of galaxies
* The New General Catalogue object NGC 81, a spiral galaxy in the constellation Andromeda

## In other fields[edit]

Eighty-one is also:

* The number of squares on a shogi playing board
* The year AD 81, 81 BC, or 1981.
* The atomic number of thallium
* The symbolic number of the Hells Angels Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.[8]
* The title of a short film by Stephen Burke: 81[importance?]
* The model number of Sinclair ZX81
* The number of the department in France called Tarn Department 81 of France (Tarn)
* The code for international direct dial phone calls to Japan
* "+81" is a song by Japanese metalcore band Crystal Lake.
* One of two ISBN Group Identifiers for books published in India
* The number of stanzas or chapters in the Tao Te Ching (in the most common arrangements).
* The number of provinces in Turkey.
* The number of prayers said in the Rosary in each night.
* "The 81" is a 1965 song by Candy and the Kisses.[importance?]
* Artemis 81 is a 1981 BBC TV science fiction drama.[9]
* 'The Eighty-One Brothers' is a Japanese fable[10]
* The number of possible divinations in the Taixuanjing

## In culture[edit]

The Arabic characters for the numerals 8 and 1 are visible in the left palm of the human hand. In China, 81 always reminds people People's Liberation Army as it was founded on August 1. 81 is used to refer to the Hells Angels Motorcycle Club, since H and A are, respectively, the 8th and 1st letters of the alphabet.

## See also[edit]

* List of highways numbered 81

## References[edit]

1. ^ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A161935 (28-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A016754 (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.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ Sloane, N. J. A. (ed.). "Sequence A005316 (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.). "Sequence A005282 (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.
9. ^ Ansorge, Peter (9 September 2011). "Aleister Reid obituary". The Guardian. London. Retrieved 24 May 2012.
10. ^ The Eighty-One Brothers, sacred-texts.com

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