513312 has 24 divisors (see below), whose sum is σ = 1347696. Its totient is φ = 171072.

The previous prime is 513311. The next prime is 513313. The reversal of 513312 is 213315.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (513311) and next prime (513313).

It is a tau number, because it is divible by the number of its divisors (24).

It is an Ulam number.

It is a junction number, because it is equal to n+sod(n) for n = 513291 and 513300.

It is not an unprimeable number, because it can be changed into a prime (513311) 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, 2578 + ... + 2769.

It is an arithmetic number, because the mean of its divisors is an integer number (56154).

2⁵¹³³¹² is an apocalyptic number.

It is an amenable number.

513312 is an abundant number, since it is smaller than the sum of its proper divisors (834384).

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

513312 is a wasteful number, since it uses less digits than its factorization.

513312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5360 (or 5352 counting only the distinct ones).

The product of its digits is 90, while the sum is 15.

The square root of 513312 is about 716.4579541048. The cubic root of 513312 is about 80.0682750482.

Adding to 513312 its reverse (213315), we get a palindrome (726627).

The spelling of 513312 in words is "five hundred thirteen thousand, three hundred twelve".