513535978045440 has 2856 divisors, whose sum is σ = 2182634883115848. Its totient is φ = 115579079884800.

The previous prime is 513535978045423. The next prime is 513535978045511. The reversal of 513535978045440 is 44540879535315.

513535978045440 is a `hidden beast` number, since 5 + 1 + 3 + 5 + 3 + 5 + 9 + 7 + 80 + 4 + 544 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 137098994909184 + 376436983136256 = 11708928^2 + 19401984^2 .

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 854469181140 + ... + 854469181740.

Almost surely, 2^{513535978045440} 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 513535978045440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1091317441557924).

513535978045440 is an abundant number, since it is smaller than the sum of its proper divisors (1669098905070408).

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

513535978045440 is an frugal number, since it uses more digits than its factorization.

513535978045440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 743 (or 691 counting only the distinct ones).

The product of its (nonzero) digits is 181440000, while the sum is 63.

The spelling of 513535978045440 in words is "five hundred thirteen trillion, five hundred thirty-five billion, nine hundred seventy-eight million, forty-five thousand, four hundred forty".