513523216440 has 192 divisors, whose sum is σ = 1808096472000. Its totient is φ = 125648603136.

The previous prime is 513523216439. The next prime is 513523216463. The reversal of 513523216440 is 44612325315.

513523216440 is a `hidden beast` number, since 5 + 1 + 3 + 5 + 2 + 3 + 2 + 1 + 644 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 513523216395 and 513523216404.

It is a congruent number.

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 47 ways as a sum of consecutive naturals, for example, 453036 + ... + 1110084.

It is an arithmetic number, because the mean of its divisors is an integer number (9417169125).

Almost surely, 2^513523216440 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 513523216440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (904048236000).

513523216440 is an abundant number, since it is smaller than the sum of its proper divisors (1294573255560).

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

513523216440 is a wasteful number, since it uses less digits than its factorization.

513523216440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 657246 (or 657239 counting only the distinct ones).

The product of its (nonzero) digits is 86400, while the sum is 36.

The spelling of 513523216440 in words is "five hundred thirteen billion, five hundred twenty-three million, two hundred sixteen thousand, four hundred forty".