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
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 astronomy

• 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

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
• 81 (八一) is referenced in flags and symbols of the People's Liberation Army as it was founded on August 1 (8/1).

See also

• List of highways numbered 81

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 .
9. Ansorge, Peter (9 September 2011). "Aleister Reid obituary". The Guardian. London. Retrieved 24 May 2012.
10. The Eighty-One Brothers, sacred-texts.com