513504 has 36 divisors (see below), whose sum is σ = 1461096. Its totient is φ = 171072.

The previous prime is 513481. The next prime is 513509. The reversal of 513504 is 405315.

It is a tau number, because it is divible by the number of its divisors (36).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513509) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 604 + ... + 1179.

It is an arithmetic number, because the mean of its divisors is an integer number (40586).

2⁵¹³⁵⁰⁴ is an apocalyptic number.

It is an amenable number.

513504 is an abundant number, since it is smaller than the sum of its proper divisors (947592).

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

513504 is a wasteful number, since it uses less digits than its factorization.

513504 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1799 (or 1788 counting only the distinct ones).

The product of its (nonzero) digits is 300, while the sum is 18.

The square root of 513504 is about 716.5919340880. The cubic root of 513504 is about 80.0782567569.

Adding to 513504 its reverse (405315), we get a palindrome (918819).

The spelling of 513504 in words is "five hundred thirteen thousand, five hundred four".