513152 has 32 divisors (see below), whose sum is σ = 1081200. Its totient is φ = 241920.

The previous prime is 513137. The next prime is 513157. The reversal of 513152 is 251315.

It is a tau number, because it is divible by the number of its divisors (32).

It is a self number, because there is not a number n which added to its sum of digits gives 513152.

It is not an unprimeable number, because it can be changed into a prime (513157) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2327 + ... + 2537.

2⁵¹³¹⁵² 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 513152, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (540600).

513152 is an abundant number, since it is smaller than the sum of its proper divisors (568048).

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

513152 is a wasteful number, since it uses less digits than its factorization.

513152 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 244 (or 232 counting only the distinct ones).

The product of its digits is 150, while the sum is 17.

The square root of 513152 is about 716.3462849768. The cubic root of 513152 is about 80.0599550562.

Adding to 513152 its reverse (251315), we get a palindrome (764467).

The spelling of 513152 in words is "five hundred thirteen thousand, one hundred fifty-two".