82592 has 24 divisors (see below), whose sum is σ = 170100. Its totient is φ = 39424.

The previous prime is 82591. The next prime is 82601. The reversal of 82592 is 29528.

It can be written as a sum of positive squares in 2 ways, for example, as 80656 + 1936 = 284^2 + 44^2 .

Its product of digits (1440) is a multiple of the sum of its prime divisors (120).

It is a zygodrome in base 4.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 82592.

It is not an unprimeable number, because it can be changed into a prime (82591) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 884 + ... + 972.

2⁸²⁵⁹² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82592, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (85050).

82592 is an abundant number, since it is smaller than the sum of its proper divisors (87508).

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

82592 is a wasteful number, since it uses less digits than its factorization.

82592 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 120 counting only the distinct ones).

The product of its digits is 1440, while the sum is 26.

The square root of 82592 is about 287.3882391470. The cubic root of 82592 is about 43.5491143852.

It can be divided in two parts, 8 and 2592, that multiplied together give a 4-th power (20736 = 12⁴).

The spelling of 82592 in words is "eighty-two thousand, five hundred ninety-two".