13585 has 16 divisors (see below), whose sum is σ = 20160. Its totient is φ = 8640.

The previous prime is 13577. The next prime is 13591. The reversal of 13585 is 58531.

13585 = 30² + 31² + ... + 40².

13585 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is not a de Polignac number, because 13585 - 2³ = 13577 is a prime.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 706 + ... + 724.

It is an arithmetic number, because the mean of its divisors is an integer number (1260).

2¹³⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

13585 is a deficient number, since it is larger than the sum of its proper divisors (6575).

13585 is a wasteful number, since it uses less digits than its factorization.

13585 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 48.

The product of its digits is 600, while the sum is 22.

The square root of 13585 is about 116.5547081846. The cubic root of 13585 is about 23.8608849985.

The spelling of 13585 in words is "thirteen thousand, five hundred eighty-five".