513206400 has 288 divisors, whose sum is σ = 1968155280. Its totient is φ = 117196800.

The previous prime is 513206377. The next prime is 513206411. The reversal of 513206400 is 4602315.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is an unprimeable number.

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 35 ways as a sum of consecutive naturals, for example, 469855 + ... + 470945.

Almost surely, 2^513206400 is an apocalyptic number.

513206400 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 513206400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (984077640).

513206400 is an abundant number, since it is smaller than the sum of its proper divisors (1454948880).

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

513206400 is a wasteful number, since it uses less digits than its factorization.

513206400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1132 (or 1108 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 21.

The square root of 513206400 is about 22654.0592389090. The cubic root of 513206400 is about 800.6278404749.

Adding to 513206400 its reverse (4602315), we get a palindrome (517808715).

The spelling of 513206400 in words is "five hundred thirteen million, two hundred six thousand, four hundred".