86 (number)

86 is:

• nonprofit^[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 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.