205820 has 24 divisors (see below), whose sum is σ = 444528. Its totient is φ = 80000.

The previous prime is 205817. The next prime is 205823. The reversal of 205820 is 28502.

205820 = T₅₁ + T₅₂ + ... + T₁₁₀.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (205817) and next prime (205823).

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (205823) 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, 695 + ... + 945.

It is an arithmetic number, because the mean of its divisors is an integer number (18522).

2²⁰⁵⁸²⁰ is an apocalyptic number.

205820 is a gapful number since it is divisible by the number (20) 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 205820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (222264).

205820 is an abundant number, since it is smaller than the sum of its proper divisors (238708).

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

205820 is a wasteful number, since it uses less digits than its factorization.

205820 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 301 (or 299 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 17.

The square root of 205820 is about 453.6738916887. The cubic root of 205820 is about 59.0421990549.

It can be divided in two parts, 205 and 820, that multiplied together give a square (168100 = 410²).

The spelling of 205820 in words is "two hundred five thousand, eight hundred twenty".