9585 has 16 divisors (see below), whose sum is σ = 17280. Its totient is φ = 5040.

The previous prime is 9551. The next prime is 9587. The reversal of 9585 is 5859.

9585 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is not a de Polignac number, because 9585 - 2⁶ = 9521 is a prime.

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

It is a plaindrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (9587) 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 15 ways as a sum of consecutive naturals, for example, 100 + ... + 170.

It is an arithmetic number, because the mean of its divisors is an integer number (1080).

2⁹⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

9585 is a deficient number, since it is larger than the sum of its proper divisors (7695).

9585 is a wasteful number, since it uses less digits than its factorization.

9585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 85 (or 79 counting only the distinct ones).

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

The square root of 9585 is about 97.9030132325. The cubic root of 9585 is about 21.2420962533.

The spelling of 9585 in words is "nine thousand, five hundred eighty-five".