513864 has 80 divisors (see below), whose sum is σ = 1575420. Its totient is φ = 155520.

The previous prime is 513841. The next prime is 513871. The reversal of 513864 is 468315.

It can be written as a sum of positive squares in 2 ways, for example, as 396900 + 116964 = 630^2 + 342^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a zygodrome in base 3.

It is an unprimeable number.

513864 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 19 ways as a sum of consecutive naturals, for example, 8394 + ... + 8454.

2⁵¹³⁸⁶⁴ is an apocalyptic number.

513864 is a gapful number since it is divisible by the number (54) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (787710).

513864 is an abundant number, since it is smaller than the sum of its proper divisors (1061556).

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

513864 is a wasteful number, since it uses less digits than its factorization.

513864 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 92 (or 79 counting only the distinct ones).

The product of its digits is 2880, while the sum is 27.

The square root of 513864 is about 716.8430790626. The cubic root of 513864 is about 80.0969657564.

The spelling of 513864 in words is "five hundred thirteen thousand, eight hundred sixty-four".