81585 has 36 divisors (see below), whose sum is σ = 168948. Its totient is φ = 36288.

The previous prime is 81569. The next prime is 81611. The reversal of 81585 is 58518.

81585 is a `hidden beast` number, since 81 + 585 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 53361 + 28224 = 231^2 + 168^2 .

It is not a de Polignac number, because 81585 - 2⁴ = 81569 is a prime.

It is a super-2 number, since 2×81585² = 13312224450, which contains 22 as substring.

It is an Ulam number.

It is a Curzon number.

81585 is a lucky number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2187 + ... + 2223.

It is an arithmetic number, because the mean of its divisors is an integer number (4693).

2⁸¹⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

81585 is an abundant number, since it is smaller than the sum of its proper divisors (87363).

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 (84474).

81585 is a wasteful number, since it uses less digits than its factorization.

81585 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 52 counting only the distinct ones).

The product of its digits is 1600, while the sum is 27.

The square root of 81585 is about 285.6308806834. The cubic root of 81585 is about 43.3713998180.

It can be divided in two parts, 815 and 85, that added together give a square (900 = 30²).

The spelling of 81585 in words is "eighty-one thousand, five hundred eighty-five".