513000000000 has 800 divisors, whose sum is σ = 1998046670400. Its totient is φ = 129600000000.

The previous prime is 512999999957. The next prime is 513000000001. The reversal of 513000000000 is 315.

It is a tau number, because it is divible by the number of its divisors (800).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a taxicab number since it can be written as a sum of two cubes in more than one way. Here 513000000000 = 1000³ + 8000³ = 4500³ + 7500³.

It is not an unprimeable number, because it can be changed into a prime (513000000001) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 26999999991 + ... + 27000000009.

It is an arithmetic number, because the mean of its divisors is an integer number (2497558338).

Almost surely, 2^513000000000 is an apocalyptic number.

513000000000 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 513000000000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (999023335200).

513000000000 is an abundant number, since it is smaller than the sum of its proper divisors (1485046670400).

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

513000000000 is an frugal number, since it uses more digits than its factorization.

513000000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 91 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 15, while the sum is 9.

Adding to 513000000000 its reverse (315), we get a palindrome (513000000315).

The spelling of 513000000000 in words is "five hundred thirteen billion", and thus it is an aban number.