39585 has 32 divisors (see below), whose sum is σ = 80640. Its totient is φ = 16128.

The previous prime is 39581. The next prime is 39607. The reversal of 39585 is 58593.

It is not a de Polignac number, because 39585 - 2² = 39581 is a prime.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors. Since it is squarefree, it is also a hoax number.

39585 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (39581) 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 31 ways as a sum of consecutive naturals, for example, 1351 + ... + 1379.

It is an arithmetic number, because the mean of its divisors is an integer number (2520).

2³⁹⁵⁸⁵ is an apocalyptic number.

39585 is a gapful number since it is divisible by the number (35) formed by its first and last digit.

It is an amenable number.

39585 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (40320).

39585 is a wasteful number, since it uses less digits than its factorization.

39585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57.

The product of its digits is 5400, while the sum is 30.

The square root of 39585 is about 198.9597949335. The cubic root of 39585 is about 34.0808341946.

The spelling of 39585 in words is "thirty-nine thousand, five hundred eighty-five".