513815328 has 288 divisors, whose sum is σ = 1717148160. Its totient is φ = 144322560.

The previous prime is 513815287. The next prime is 513815329. The reversal of 513815328 is 823518315.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 513815292 and 513815301.

It is not an unprimeable number, because it can be changed into a prime (513815329) 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, 2205100 + ... + 2205332.

It is an arithmetic number, because the mean of its divisors is an integer number (5962320).

Almost surely, 2^513815328 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 513815328, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (858574080).

513815328 is an abundant number, since it is smaller than the sum of its proper divisors (1203332832).

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

513815328 is a wasteful number, since it uses less digits than its factorization.

513815328 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 312 (or 301 counting only the distinct ones).

The product of its digits is 28800, while the sum is 36.

The square root of 513815328 is about 22667.4949652581. The cubic root of 513815328 is about 800.9443681058.

The spelling of 513815328 in words is "five hundred thirteen million, eight hundred fifteen thousand, three hundred twenty-eight".