513072 has 60 divisors (see below), whose sum is σ = 1644240. Its totient is φ = 146304.

The previous prime is 513067. The next prime is 513083. The reversal of 513072 is 270315.

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

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 754 + ... + 1262.

It is an arithmetic number, because the mean of its divisors is an integer number (27404).

2⁵¹³⁰⁷² 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 513072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (822120).

513072 is an abundant number, since it is smaller than the sum of its proper divisors (1131168).

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

513072 is a wasteful number, since it uses less digits than its factorization.

513072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 530 (or 521 counting only the distinct ones).

The product of its (nonzero) digits is 210, while the sum is 18.

The square root of 513072 is about 716.2904438843. The cubic root of 513072 is about 80.0557944116.

Adding to 513072 its reverse (270315), we get a palindrome (783387).

The spelling of 513072 in words is "five hundred thirteen thousand, seventy-two".