85509 has 8 divisors (see below), whose sum is σ = 126720. Its totient is φ = 56988.

The previous prime is 85487. The next prime is 85513. The reversal of 85509 is 90558.

It is not a de Polignac number, because 85509 - 2⁷ = 85381 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (27), and also a Moran number because the ratio is a prime number: 3167 = 85509 / (8 + 5 + 5 + 0 + 9).

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 (85549) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1557 + ... + 1610.

It is an arithmetic number, because the mean of its divisors is an integer number (15840).

2⁸⁵⁵⁰⁹ is an apocalyptic number.

It is an amenable number.

85509 is a deficient number, since it is larger than the sum of its proper divisors (41211).

85509 is a wasteful number, since it uses less digits than its factorization.

85509 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3176 (or 3170 counting only the distinct ones).

The product of its (nonzero) digits is 1800, while the sum is 27.

The square root of 85509 is about 292.4192196146. The cubic root of 85509 is about 44.0558862867.

The spelling of 85509 in words is "eighty-five thousand, five hundred nine".