513363312 has 480 divisors, whose sum is σ = 1963207680. Its totient is φ = 125452800.

The previous prime is 513363239. The next prime is 513363341. The reversal of 513363312 is 213363315.

It is a happy number.

513363312 is a `hidden beast` number, since 5 + 13 + 3 + 633 + 12 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 8415762 + ... + 8415822.

It is an arithmetic number, because the mean of its divisors is an integer number (4090016).

Almost surely, 2^513363312 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 513363312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (981603840).

513363312 is an abundant number, since it is smaller than the sum of its proper divisors (1449844368).

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

513363312 is a wasteful number, since it uses less digits than its factorization.

513363312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 107 counting only the distinct ones).

The product of its digits is 4860, while the sum is 27.

The square root of 513363312 is about 22657.5221946267. The cubic root of 513363312 is about 800.7094290354.

The spelling of 513363312 in words is "five hundred thirteen million, three hundred sixty-three thousand, three hundred twelve".