513905581728 has 576 divisors, whose sum is σ = 1900791567360. Its totient is φ = 132214325760.

The previous prime is 513905581727. The next prime is 513905581747. The reversal of 513905581728 is 827185509315.

513905581728 is a `hidden beast` number, since 5 + 1 + 39 + 0 + 5 + 581 + 7 + 28 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (513905581727) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 78300175 + ... + 78306737.

It is an arithmetic number, because the mean of its divisors is an integer number (3299985360).

Almost surely, 2^513905581728 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 513905581728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (950395783680).

513905581728 is an abundant number, since it is smaller than the sum of its proper divisors (1386885985632).

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

513905581728 is a wasteful number, since it uses less digits than its factorization.

513905581728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6718 (or 6693 counting only the distinct ones).

The product of its (nonzero) digits is 3024000, while the sum is 54.

The spelling of 513905581728 in words is "five hundred thirteen billion, nine hundred five million, five hundred eighty-one thousand, seven hundred twenty-eight".