85617 has 20 divisors (see below), whose sum is σ = 147136. Its totient is φ = 48600.

The previous prime is 85607. The next prime is 85619. The reversal of 85617 is 71658.

It is not a de Polignac number, because 85617 - 2⁴ = 85601 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a Duffinian number.

85617 is a lucky number.

It is a zygodrome in base 3.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (85619) by changing a digit.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 492 + ... + 642.

2⁸⁵⁶¹⁷ is an apocalyptic number.

It is an amenable number.

85617 is a deficient number, since it is larger than the sum of its proper divisors (61519).

85617 is a wasteful number, since it uses less digits than its factorization.

85617 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 170 (or 161 counting only the distinct ones).

The product of its digits is 1680, while the sum is 27.

The square root of 85617 is about 292.6038277262. The cubic root of 85617 is about 44.0744263778.

It can be divided in two parts, 8 and 5617, that added together give a square (5625 = 75²).

The spelling of 85617 in words is "eighty-five thousand, six hundred seventeen".