513213 has 16 divisors (see below), whose sum is σ = 751680. Its totient is φ = 310016.

The previous prime is 513203. The next prime is 513239. The reversal of 513213 is 312315.

It is a happy number.

It is a cyclic number.

It is not a de Polignac number, because 513213 - 2¹⁶ = 447677 is a prime.

It is a Curzon number.

It is a junction number, because it is equal to n+sod(n) for n = 513192 and 513201.

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 513213.

It is not an unprimeable number, because it can be changed into a prime (513203) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1306 + ... + 1652.

It is an arithmetic number, because the mean of its divisors is an integer number (46980).

2⁵¹³²¹³ is an apocalyptic number.

It is an amenable number.

513213 is a deficient number, since it is larger than the sum of its proper divisors (238467).

513213 is a wasteful number, since it uses less digits than its factorization.

513213 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 396.

The product of its digits is 90, while the sum is 15.

The square root of 513213 is about 716.3888608849. The cubic root of 513213 is about 80.0631272571.

Adding to 513213 its reverse (312315), we get a palindrome (825528).

The spelling of 513213 in words is "five hundred thirteen thousand, two hundred thirteen".