86 (number)

{{Infobox number

| number = 86

| divisor = 1, 2, 43, 86

}}

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

In mathematics

86 is:

  • nontotient{{Cite OEIS|A005277|Nontotients}} and a noncototient.{{Cite OEIS|A005278|Noncototients}}
  • the 25th distinct semiprime{{Cite OEIS|A006881|Squarefree semiprimes: Numbers that are the product of two distinct primes}} 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.{{Cite OEIS|A056809|Numbers k such that k, k+1 and k+2 are products of two primes}}
  • 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.{{Cite OEIS|A059756|Erdős-Woods numbers}}
  • a happy number{{Cite OEIS|A007770|Happy numbers}} and a self number in base 10.{{Cite OEIS|A003052|Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m)}}
  • 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).{{Cite OEIS|A000931|Padovan sequence}}

It is conjectured that 86 is the largest n for which the decimal expansion of 2n contains no 0.{{Cite OEIS|A007377|Numbers k such that the decimal expansion of 2^k contains no 0}}

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 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.{{Cite web|date=2013-08-13|title=Where Did the Term 86 Come From?|url=https://www.mentalfloss.com/article/51880/where-did-term-86-come|access-date=2021-10-30|website=www.mentalfloss.com|language=en}}
  • 86, particularly "Hachi-Roku (ハチロク)," is often used in Japan as the nickname for the Toyota AE86.
  • The international calling code for Mainland China
  • 86 is the racing number of Chick Hicks — a character from Disney Pixar's Cars franchise.

Notes

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{{Integers|zero}}

Category:Integers