513856000000 has 728 divisors, whose sum is σ = 1556270079488. Its totient is φ = 165888000000.

The previous prime is 513855999971. The next prime is 513856000003. The reversal of 513856000000 is 658315.

It is a hoax number, since the sum of its digits (28) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (28).

It is a taxicab number since it can be written as a sum of two cubes in more than one way. Here 513856000000 = 3400³ + 7800³ = 5200³ + 7200³.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513856000003) by changing a digit.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 13887999982 + ... + 13888000018.

Almost surely, 2^513856000000 is an apocalyptic number.

513856000000 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513856000000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (778135039744).

513856000000 is an abundant number, since it is smaller than the sum of its proper divisors (1042414079488).

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

513856000000 is an frugal number, since it uses more digits than its factorization.

513856000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 129 (or 82 counting only the distinct ones).

The product of its (nonzero) digits is 3600, while the sum is 28.

Adding to 513856000000 its reverse (658315), we get a palindrome (513856658315).

The spelling of 513856000000 in words is "five hundred thirteen billion, eight hundred fifty-six million", and thus it is an aban number.