• 85 can be written using four 4's:

85 has 4 divisors (see below), whose sum is σ = 108. Its totient is φ = 64.

The previous prime is 83. The next prime is 89. The reversal of 85 is 58.

85 = T_{6} + T_{7} +
T_{8}.

85 is nontrivially palindromic in base 2, base 4, base 7 and base 16.

85 is an esthetic number in base 2, base 11 and base 13, because in such bases its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes, and also an emirpimes, since its reverse is a distinct semiprime: 58 = 2 ⋅29.

It can be written as a sum of positive squares in 2 ways, for example, as 49 + 36 = 7^2 + 6^2 .

It is a 3-Lehmer number, since φ(85) divides (85-1)^{3}.

It is a cyclic number.

It is not a de Polignac number, because 85 - 2^{1} = 83 is a prime.

It is a Smith number, since the sum of its digits (13) coincides with the sum of the digits of its prime factors. Since it is squarefree, it is also a hoax number.

85 is an idoneal number.

It is the 8-th Jacobsthal number.

It is a magnanimous number.

It is an alternating number because its digits alternate between even and odd.

It is a Duffinian number.

85 is an undulating number in base 2 and base 7.

85 is a nontrivial repdigit in base 4 and base 16.

It is a plaindrome in base 4, base 8, base 11, base 13, base 15 and base 16.

It is a nialpdrome in base 4, base 5, base 6, base 10, base 12, base 14 and base 16.

It is a zygodrome in base 4 and base 16.

It is a congruent number.

It is a panconsummate number.

It is a nontrivial repunit in base 4.

In principle, a polygon with 85 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 4 + ... + 13.

It is an arithmetic number, because the mean of its divisors is an integer number (27).

85 is the 5-th decagonal number.

85 is the 8-th centered triangular number and also the 7-th centered square number.

It is an amenable number.

85 is a deficient number, since it is larger than the sum of its proper divisors (23).

85 is a wasteful number, since it uses less digits than its factorization.

85 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 22.

The product of its digits is 40, while the sum is 13.

The square root of 85 is about 9.2195444573. The cubic root of 85 is about 4.3968296722.

Adding to 85 its product of digits (40), we get a cube (125 = 5^{3}).

Subtracting from 85 its product of digits (40), we obtain a triangular number (45 = T_{9}).

Subtracting from 85 its reverse (58), we obtain a cube (27 = 3^{3}).

The spelling of 85 in words is "eighty-five", and thus it is an aban number, an oban number, and an uban number.

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