509520 has 80 divisors (see below), whose sum is σ = 1732032. Its totient is φ = 122880.

The previous prime is 509513. The next prime is 509521. The reversal of 509520 is 25905.

It is a tau number, because it is divible by the number of its divisors (80).

It is a super-2 number, since 2×509520² = 519221260800, which contains 22 as substring.

It is a plaindrome in base 13.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509521) by changing a digit.

509520 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2544 + ... + 2736.

2⁵⁰⁹⁵²⁰ 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 509520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (866016).

509520 is an abundant number, since it is smaller than the sum of its proper divisors (1222512).

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

509520 is a wasteful number, since it uses less digits than its factorization.

509520 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 220 (or 214 counting only the distinct ones).

The product of its (nonzero) digits is 450, while the sum is 21.

The square root of 509520 is about 713.8066965222. The cubic root of 509520 is about 79.8706242200.

It can be divided in two parts, 5095 and 20, that added together give a palindrome (5115).

The spelling of 509520 in words is "five hundred nine thousand, five hundred twenty".