513684 has 36 divisors (see below), whose sum is σ = 1368640. Its totient is φ = 162000.

The previous prime is 513683. The next prime is 513691. The reversal of 513684 is 486315.

It is a tau number, because it is divible by the number of its divisors (36).

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513683) 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 11 ways as a sum of consecutive naturals, for example, 309 + ... + 1059.

2⁵¹³⁶⁸⁴ 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 513684, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (684320).

513684 is an abundant number, since it is smaller than the sum of its proper divisors (854956).

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

513684 is a wasteful number, since it uses less digits than its factorization.

513684 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 780 (or 775 counting only the distinct ones).

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

The square root of 513684 is about 716.7175175758. The cubic root of 513684 is about 80.0876123493.

Adding to 513684 its reverse (486315), we get a palindrome (999999).

It can be divided in two parts, 5 and 13684, that added together give a square (13689 = 117²).

The spelling of 513684 in words is "five hundred thirteen thousand, six hundred eighty-four".