513128448 has 288 divisors, whose sum is σ = 1752922080. Its totient is φ = 141557760.

The previous prime is 513128443. The next prime is 513128449. The reversal of 513128448 is 844821315.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513128443) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5289936 + ... + 5290032.

It is an arithmetic number, because the mean of its divisors is an integer number (6086535).

Almost surely, 2^513128448 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 513128448, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (876461040).

513128448 is an abundant number, since it is smaller than the sum of its proper divisors (1239793632).

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

513128448 is a wasteful number, since it uses less digits than its factorization.

513128448 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 173 (or 150 counting only the distinct ones).

The product of its digits is 30720, while the sum is 36.

The square root of 513128448 is about 22652.3386872084. The cubic root of 513128448 is about 800.5873020732.

The spelling of 513128448 in words is "five hundred thirteen million, one hundred twenty-eight thousand, four hundred forty-eight".