513524 has 18 divisors (see below), whose sum is σ = 988722. Its totient is φ = 233200.

The previous prime is 513511. The next prime is 513529. The reversal of 513524 is 425315.

It can be written as a sum of positive squares in only one way, i.e., 465124 + 48400 = 682^2 + 220^2 .

It is a junction number, because it is equal to n+sod(n) for n = 513496 and 513505.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 513524.

It is not an unprimeable number, because it can be changed into a prime (513529) by changing a digit.

513524 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 47 + ... + 1014.

It is an arithmetic number, because the mean of its divisors is an integer number (54929).

2⁵¹³⁵²⁴ is an apocalyptic number.

It is an amenable number.

513524 is a deficient number, since it is larger than the sum of its proper divisors (475198).

513524 is a wasteful number, since it uses less digits than its factorization.

513524 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1087 (or 1074 counting only the distinct ones).

The product of its digits is 600, while the sum is 20.

The square root of 513524 is about 716.6058888957. The cubic root of 513524 is about 80.0792963751.

Adding to 513524 its reverse (425315), we get a palindrome (938839).

Subtracting from 513524 its reverse (425315), we obtain a square (88209 = 297²).

The spelling of 513524 in words is "five hundred thirteen thousand, five hundred twenty-four".