513104400 has 90 divisors (see below), whose sum is σ = 1780627290. Its totient is φ = 136826880.

The previous prime is 513104399. The next prime is 513104413. The reversal of 513104400 is 4401315.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 159062544 + 354041856 = 12612^2 + 18816^2 .

It is a tau number, because it is divible by the number of its divisors (90).

It is a super-2 number, since 2×513104400² = 526552250598720000, which contains 22 as substring.

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 (13) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 67665 + ... + 74864.

Almost surely, 2^513104400 is an apocalyptic number.

513104400 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

513104400 is an abundant number, since it is smaller than the sum of its proper divisors (1267522890).

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

513104400 is a wasteful number, since it uses less digits than its factorization.

513104400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 142553 (or 142539 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 513104400 is about 22651.8078748695. The cubic root of 513104400 is about 800.5747952475.

Adding to 513104400 its reverse (4401315), we get a palindrome (517505715).

The spelling of 513104400 in words is "five hundred thirteen million, one hundred four thousand, four hundred".