513728 has 28 divisors (see below), whose sum is σ = 1066800. Its totient is φ = 244992.

The previous prime is 513727. The next prime is 513731. The reversal of 513728 is 827315.

513728 is nontrivially palindromic in base 3.

It is an Ulam number.

It is a zygodrome in base 3.

It is a junction number, because it is equal to n+sod(n) for n = 513697 and 513706.

It is not an unprimeable number, because it can be changed into a prime (513727) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1298 + ... + 1646.

It is an arithmetic number, because the mean of its divisors is an integer number (38100).

2⁵¹³⁷²⁸ 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 513728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (533400).

513728 is an abundant number, since it is smaller than the sum of its proper divisors (553072).

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

513728 is a wasteful number, since it uses less digits than its factorization.

513728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 384 (or 374 counting only the distinct ones).

The product of its digits is 1680, while the sum is 26.

The square root of 513728 is about 716.7482124149. The cubic root of 513728 is about 80.0898989394.

The spelling of 513728 in words is "five hundred thirteen thousand, seven hundred twenty-eight".