513313920 has 384 divisors, whose sum is σ = 2100384000. Its totient is φ = 113025024.

The previous prime is 513313901. The next prime is 513313921. The reversal of 513313920 is 29313315.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (384).

It is not an unprimeable number, because it can be changed into a prime (513313921) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 1169061 + ... + 1169499.

It is an arithmetic number, because the mean of its divisors is an integer number (5469750).

Almost surely, 2^513313920 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513313920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1050192000).

513313920 is an abundant number, since it is smaller than the sum of its proper divisors (1587070080).

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

513313920 is a wasteful number, since it uses less digits than its factorization.

513313920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 500 (or 485 counting only the distinct ones).

The product of its (nonzero) digits is 2430, while the sum is 27.

The square root of 513313920 is about 22656.4321992674. The cubic root of 513313920 is about 800.6837487764.

The spelling of 513313920 in words is "five hundred thirteen million, three hundred thirteen thousand, nine hundred twenty".