513104000 has 64 divisors (see below), whose sum is σ = 1275744600. Its totient is φ = 205235200.

The previous prime is 513103939. The next prime is 513104057. The reversal of 513104000 is 401315.

It can be written as a sum of positive squares in 4 ways, for example, as 239135296 + 273968704 = 15464^2 + 16552^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 35 + ... + 32034.

Almost surely, 2^513104000 is an apocalyptic number.

513104000 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 513104000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (637872300).

513104000 is an abundant number, since it is smaller than the sum of its proper divisors (762640600).

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

513104000 is an equidigital number, since it uses as much as digits as its factorization.

513104000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32098 (or 32076 counting only the distinct ones).

The product of its (nonzero) digits is 60, while the sum is 14.

The square root of 513104000 is about 22651.7990455504. The cubic root of 513104000 is about 800.5745872131.

Adding to 513104000 its reverse (401315), we get a palindrome (513505315).

The spelling of 513104000 in words is "five hundred thirteen million, one hundred four thousand".