7585 has 8 divisors (see below), whose sum is σ = 9576. Its totient is φ = 5760.

The previous prime is 7583. The next prime is 7589. The reversal of 7585 is 5857.

It can be written as a sum of positive squares in 4 ways, for example, as 529 + 7056 = 23^2 + 84^2 .

It is a sphenic number, since it is the product of 3 distinct primes.

It is not a de Polignac number, because 7585 - 2¹ = 7583 is a prime.

It is a Duffinian number.

7585 is a lucky number.

It is a plaindrome in base 9 and base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7583) 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, 165 + ... + 205.

It is an arithmetic number, because the mean of its divisors is an integer number (1197).

2⁷⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

7585 is a deficient number, since it is larger than the sum of its proper divisors (1991).

7585 is a wasteful number, since it uses less digits than its factorization.

7585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 83.

The product of its digits is 1400, while the sum is 25.

The square root of 7585 is about 87.0919054792. The cubic root of 7585 is about 19.6480080942.

Subtracting from 7585 its reverse (5857), we obtain a cube (1728 = 12³).

It can be divided in two parts, 7 and 585, that multiplied together give a triangular number (4095 = T₉₀).

The spelling of 7585 in words is "seven thousand, five hundred eighty-five".