513013200 has 240 divisors, whose sum is σ = 1894938240. Its totient is φ = 116213760.

The previous prime is 513013181. The next prime is 513013211. The reversal of 513013200 is 2310315.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 513013200.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1318606 + ... + 1318994.

It is an arithmetic number, because the mean of its divisors is an integer number (7895576).

Almost surely, 2^513013200 is an apocalyptic number.

513013200 is a gapful number since it is divisible by the number (50) 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 513013200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (947469120).

513013200 is an abundant number, since it is smaller than the sum of its proper divisors (1381925040).

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

513013200 is a wasteful number, since it uses less digits than its factorization.

513013200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 574 (or 563 counting only the distinct ones).

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

The square root of 513013200 is about 22649.7947010563. The cubic root of 513013200 is about 800.5273606204.

Adding to 513013200 its reverse (2310315), we get a palindrome (515323515).

The spelling of 513013200 in words is "five hundred thirteen million, thirteen thousand, two hundred".