205209 has 9 divisors (see below), whose sum is σ = 298389. Its totient is φ = 135900.

The previous prime is 205201. The next prime is 205211. The reversal of 205209 is 902502.

205209 = T₄₅₂ + T₄₅₃.

The square root of 205209 is 453.

It is a perfect power (a square), and thus also a powerful number.

It is a tau number, because it is divible by the number of its divisors (9).

It is not a de Polignac number, because 205209 - 2³ = 205201 is a prime.

It is a super-2 number, since 2×205209² = 84221467362, which contains 22 as substring.

It is a junction number, because it is equal to n+sod(n) for n = 205191 and 205200.

It is not an unprimeable number, because it can be changed into a prime (205201) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 1284 + ... + 1434.

2²⁰⁵²⁰⁹ is an apocalyptic number.

205209 is the 453-rd square number.

205209 is the 227-th centered octagonal number.

It is an amenable number.

205209 is a deficient number, since it is larger than the sum of its proper divisors (93180).

205209 is an equidigital number, since it uses as much as digits as its factorization.

205209 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 308 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The cubic root of 205209 is about 58.9837166593.

It can be divided in two parts, 205 and 209, that added together give a palindrome (414).

The spelling of 205209 in words is "two hundred five thousand, two hundred nine".