513974286400 has 63 divisors (see below), whose sum is σ = 1264768545261. Its totient is φ = 205578243840.

The previous prime is 513974286361. The next prime is 513974286409. The reversal of 513974286400 is 4682479315.

It is a happy number.

The square root of 513974286400 is 716920.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 185030743104 + 328943543296 = 430152^2 + 573536^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (513974286409) by changing a digit.

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 8 ways as a sum of consecutive naturals, for example, 28667839 + ... + 28685761.

It is a 1-persistent number, because it is pandigital, but 2⋅513974286400 = 1027948572800 is not.

Almost surely, 2^513974286400 is an apocalyptic number.

513974286400 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

513974286400 is the 716920-th square number.

It is an amenable number.

513974286400 is an abundant number, since it is smaller than the sum of its proper divisors (750794258861).

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

513974286400 is an frugal number, since it uses more digits than its factorization.

513974286400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 35868 (or 17930 counting only the distinct ones).

The product of its (nonzero) digits is 1451520, while the sum is 49.

Multiplying 513974286400 by its sum of digits (49), we get a square (25184740033600 = 5018440²).

The spelling of 513974286400 in words is "five hundred thirteen billion, nine hundred seventy-four million, two hundred eighty-six thousand, four hundred".