205392 has 40 divisors (see below), whose sum is σ = 580320. Its totient is φ = 62080.

The previous prime is 205391. The next prime is 205397. The reversal of 205392 is 293502.

205392 is nontrivially palindromic in base 5.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 205392.

It is not an unprimeable number, because it can be changed into a prime (205391) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 334 + ... + 722.

It is an arithmetic number, because the mean of its divisors is an integer number (14508).

2²⁰⁵³⁹² is an apocalyptic number.

205392 is a gapful number since it is divisible by the number (22) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 205392, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (290160).

205392 is an abundant number, since it is smaller than the sum of its proper divisors (374928).

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

205392 is a wasteful number, since it uses less digits than its factorization.

205392 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 411 (or 405 counting only the distinct ones).

The product of its (nonzero) digits is 540, while the sum is 21.

The square root of 205392 is about 453.2019417434. The cubic root of 205392 is about 59.0012448267.

Adding to 205392 its reverse (293502), we get a palindrome (498894).

It can be divided in two parts, 2053 and 92, that added together give a triangular number (2145 = T₆₅).

The spelling of 205392 in words is "two hundred five thousand, three hundred ninety-two".