85

85 = 5 x 17.

85 is a Smith number because the sum of its digits is equal to sum of the digits in its prime factorization: 8 + 5 = 13 = 5 + 1 + 7.

85 is a centered triangular number. Such a number can be represented by a dot in the center, with all other dots surrounding the center in successive triangular layers. The first few triangular numbers are: 1, 4, 10, 19, 31, 46, 64, 85, 109, . . .

85 is the largest known n for which 1² + 2² + 3² + . . . + n² = 1 + 2 + 3 + . . . + m has a solution.

There are 85 ways to tie a tie, according to a book by Thomas Fink and Yong Mao.

Sources: Wolfram MathWorld ; What's Special About This Number?