86 (number)

← 85 86 87 →
← 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-six
Ordinal	86th (eighty-sixth)
Factorization	2 × 43
Divisors	1, 2, 43, 86
Greek numeral	ΠϚ´
Roman numeral	LXXXVI, lxxxvi
Binary	10101102
Ternary	100123
Senary	2226
Octal	1268
Duodecimal	7212
Hexadecimal	5616

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 ^[3] 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. ^[4]
• 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. ^[5]
• a happy number ^[6] and a self number in base 10. ^[7]
• 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). ^[8]

It is conjectured that 86 is the largest n for which the decimal expansion of 2ⁿ contains no 0. ^[9]

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. ^[10]
• 86, particularly "Hachi-Roku (ハチロク)," is often used in Japan as the nickname for the Toyota AE86.

Notes

1. Sloane, N. J. A. (ed.). "SequenceA005277(Nontotients)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA005278(Noncototients)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA006881(Squarefree semiprimes: Numbers that are the product of two distinct primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA056809(Numbers k such that k, k+1 and k+2 are products of two primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA059756(Erdős-Woods numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA007770(Happy numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
7. Sloane, N. J. A. (ed.). "SequenceA003052(Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
8. Sloane, N. J. A. (ed.). "SequenceA000931(Padovan sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
9. Sloane, N. J. A. (ed.). "SequenceA007377(Numbers k such that the decimal expansion of 2^k contains no 0)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
10. "Where Did the Term 86 Come From?". www.mentalfloss.com. 2013-08-13. Retrieved 2021-10-30.