513533952 has 192 divisors, whose sum is σ = 1568548800. Its totient is φ = 165888000.

The previous prime is 513533947. The next prime is 513533953. The reversal of 513533952 is 259335315.

It is a happy number.

513533952 is a `hidden beast` number, since 513 + 53 + 3 + 95 + 2 = 666.

It is a tau number, because it is divible by the number of its divisors (192).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (513533953) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 2045827 + ... + 2046077.

It is an arithmetic number, because the mean of its divisors is an integer number (8169525).

Almost surely, 2^513533952 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 513533952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (784274400).

513533952 is an abundant number, since it is smaller than the sum of its proper divisors (1055014848).

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

513533952 is a wasteful number, since it uses less digits than its factorization.

513533952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 319 (or 293 counting only the distinct ones).

The product of its digits is 60750, while the sum is 36.

The square root of 513533952 is about 22661.2875185855. The cubic root of 513533952 is about 800.7981367906.

The spelling of 513533952 in words is "five hundred thirteen million, five hundred thirty-three thousand, nine hundred fifty-two".