205309 has 8 divisors (see below), whose sum is σ = 234360. Its totient is φ = 178176.

The previous prime is 205307. The next prime is 205319. The reversal of 205309 is 903502.

It can be written as a sum of positive squares in 4 ways, for example, as 100 + 205209 = 10^2 + 453^2 .

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

It is a cyclic number.

It is not a de Polignac number, because 205309 - 2¹ = 205307 is a prime.

It is a Duffinian number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (205307) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 244 + ... + 685.

It is an arithmetic number, because the mean of its divisors is an integer number (29295).

2²⁰⁵³⁰⁹ is an apocalyptic number.

It is an amenable number.

205309 is a deficient number, since it is larger than the sum of its proper divisors (29051).

205309 is a wasteful number, since it uses less digits than its factorization.

205309 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 959.

The product of its (nonzero) digits is 270, while the sum is 19.

The square root of 205309 is about 453.1103618325. The cubic root of 205309 is about 58.9932961836.

It can be divided in two parts, 20 and 5309, that added together give a square (5329 = 73²).

The spelling of 205309 in words is "two hundred five thousand, three hundred nine".