205416 has 40 divisors (see below), whose sum is σ = 577170. Its totient is φ = 68256.

The previous prime is 205399. The next prime is 205417. The reversal of 205416 is 614502.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 202500 + 2916 = 450^2 + 54^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (205417) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 490 + ... + 806.

2²⁰⁵⁴¹⁶ 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 205416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (288585).

205416 is an abundant number, since it is smaller than the sum of its proper divisors (371754).

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

205416 is a wasteful number, since it uses less digits than its factorization.

205416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 335 (or 322 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 205416 is about 453.2284192325. The cubic root of 205416 is about 59.0035428304.

Adding to 205416 its reverse (614502), we get a palindrome (819918).

The spelling of 205416 in words is "two hundred five thousand, four hundred sixteen".