513641689344 has 729 divisors, whose sum is σ = 1811843899047. Its totient is φ = 144897113088.

The previous prime is 513641689291. The next prime is 513641689367. The reversal of 513641689344 is 443986146315.

It is a happy number.

The square root of 513641689344 is 716688.

It is a perfect power (a square), and thus also a powerful number.

513641689344 is a `hidden beast` number, since 5 + 136 + 4 + 168 + 9 + 344 = 666.

It is a tau number, because it is divible by the number of its divisors (729).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 6501793497 + ... + 6501793575.

Almost surely, 2^513641689344 is an apocalyptic number.

513641689344 is a gapful number since it is divisible by the number (54) formed by its first and last digit.

513641689344 is the 716688-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513641689344

513641689344 is an abundant number, since it is smaller than the sum of its proper divisors (1298202209703).

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

513641689344 is an frugal number, since it uses more digits than its factorization.

513641689344 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 212 (or 91 counting only the distinct ones).

The product of its digits is 7464960, while the sum is 54.

The spelling of 513641689344 in words is "five hundred thirteen billion, six hundred forty-one million, six hundred eighty-nine thousand, three hundred forty-four".