513888 has 48 divisors (see below), whose sum is σ = 1388016. Its totient is φ = 166400.

The previous prime is 513881. The next prime is 513899. The reversal of 513888 is 888315.

It is a tau number, because it is divible by the number of its divisors (48).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 513888.

It is not an unprimeable number, because it can be changed into a prime (513881) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 5038 + ... + 5138.

It is an arithmetic number, because the mean of its divisors is an integer number (28917).

2⁵¹³⁸⁸⁸ 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 513888, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (694008).

513888 is an abundant number, since it is smaller than the sum of its proper divisors (874128).

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

513888 is a wasteful number, since it uses less digits than its factorization.

513888 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 167 (or 159 counting only the distinct ones).

The product of its digits is 7680, while the sum is 33.

The square root of 513888 is about 716.8598189325. The cubic root of 513888 is about 80.0982127123.

The spelling of 513888 in words is "five hundred thirteen thousand, eight hundred eighty-eight".