81 (number)

← 80 81 82 →
→
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
  9 and the second fourth-power of a prime; 3
  ⁴.
• with an
  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

, 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

• 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

  

  )
• 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