512072 has 36 divisors (see below), whose sum is σ = 1103235. Its totient is φ = 222640.

The previous prime is 512059. The next prime is 512093. The reversal of 512072 is 270215.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 256036 + 256036 = 506^2 + 506^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=506.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 512072.

It is an unprimeable number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 22253 + ... + 22275.

512072 is a Friedman number, since it can be written as 2*(507-1)^2, using all its digits and the basic arithmetic operations.

2⁵¹²⁰⁷² is an apocalyptic number.

512072 is the 383-rd centered heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 512072

512072 is an abundant number, since it is smaller than the sum of its proper divisors (591163).

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

512072 is a wasteful number, since it uses less digits than its factorization.

512072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 74 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 140, while the sum is 17.

The square root of 512072 is about 715.5920625608. The cubic root of 512072 is about 80.0037498242.

Adding to 512072 its reverse (270215), we get a palindrome (782287).

The spelling of 512072 in words is "five hundred twelve thousand, seventy-two".