86 (number)

86 (eighty-six) is the natural number following 85 and preceding 87.

In mathematics

86 is:

• nontotient^[1] and a noncototient.^[2]
• the 25th distinct semiprime and the 13th of the form (2.q).
• together with 85 and 87, forms the middle semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33, 34, 35.^[3]
• an Erdős–Woods number, since it is possible to find sequences of 86 consecutive integers such that each inner member shares a factor with either the first or the last member.^[4]
• a happy number^[5] and a self number in base 10.^[6]
• with an aliquot sum of 46; itself a semiprime, within an aliquot sequence of seven members (86,46,26,16,15,9,4,3,1,0) in the Prime 3-aliquot tree.

It appears in the Padovan sequence, preceded by the terms 37, 49, 65 (it is the sum of the first two of these).^[7]

It is conjectured that 86 is the largest n for which the decimal expansion of 2ⁿ contains no 0.^[8]

86 = (8 × 6 = 48) + (4 × 8 = 32) + (3 × 2 = 6). That is, 86 is equal to the sum of the numbers formed in calculating its multiplicative persistence.

In science

• 86 is the atomic number of radon.
• There are 86 metals on the modern periodic table.

In other fields

• In American English, and particularly in the food service industry, 86 has become a slang term referring to an item being out of stock or discontinued, and by extension to a person no longer welcome on the premises.^[9]
• The number of the French department Vienne. This number is also reflected in the department's postal code and in the name of a local basketball club, Poitiers Basket 86.
• +86 is the code for international direct dial phone calls to China .
• An art gallery in Ventura, California, displaying art pieces from such artists Billy Childish, Stacy Lande and Derek Hess, most of which include the number *86 hidden or overtly shown in the art, and some of which fall under the genre of lowbrow.
• 86 is the device number for a lockout relay function in electrical engineering electrical circuit protection schemes.
• 86 is often used in Japan as the nickname for the Toyota AE86.
• 86 is the name of a series of Japanese science fiction light novels written by Asato Asato, later adapted as a manga and an anime.

See also

• List of highways numbered 86

Notes

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