513115200 has 252 divisors, whose sum is σ = 1964736228. Its totient is φ = 126259200.

The previous prime is 513115181. The next prime is 513115219. The reversal of 513115200 is 2511315.

513115200 is a `hidden beast` number, since 513 + 1 + 152 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (513115181) and next prime (513115219).

It can be written as a sum of positive squares in 6 ways, for example, as 94012416 + 419102784 = 9696^2 + 20472^2 .

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

It is an unprimeable number.

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 35 ways as a sum of consecutive naturals, for example, 185830 + ... + 188570.

Almost surely, 2^513115200 is an apocalyptic number.

513115200 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 513115200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (982368114).

513115200 is an abundant number, since it is smaller than the sum of its proper divisors (1451621028).

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

513115200 is a wasteful number, since it uses less digits than its factorization.

513115200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2782 (or 2764 counting only the distinct ones).

The product of its (nonzero) digits is 150, while the sum is 18.

The square root of 513115200 is about 22652.0462651832. The cubic root of 513115200 is about 800.5804121337.

Adding to 513115200 its reverse (2511315), we get a palindrome (515626515).

It can be divided in two parts, 513115 and 200, that added together give a palindrome (513315).

The spelling of 513115200 in words is "five hundred thirteen million, one hundred fifteen thousand, two hundred".