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86 (number)

FieldValue
number86
divisor1, 2, 43, 86

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

In mathematics

86 is:

  • nontotient and a noncototient.
  • 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.
  • 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.
  • a happy number and a self number in base 10.
  • 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).

It is conjectured that 86 is the largest n for which the decimal expansion of 2n 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.
  • 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

References

  1. {{Cite OEIS. A005277. Nontotients
  2. {{Cite OEIS. A005278. Noncototients
  3. {{Cite OEIS. A006881. Squarefree semiprimes: Numbers that are the product of two distinct primes
  4. {{Cite OEIS. A056809. Numbers k such that k, k+1 and k+2 are products of two primes
  5. {{Cite OEIS. A059756. Erdős-Woods numbers
  6. {{Cite OEIS. A007770. Happy numbers
  7. {{Cite OEIS. A003052. Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m)
  8. {{Cite OEIS. A000931. Padovan sequence
  9. {{Cite OEIS. A007377. Numbers k such that the decimal expansion of 2^k contains no 0
  10. (2013-08-13). "Where Did the Term 86 Come From?".
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