513216 has 98 divisors (see below), whose sum is σ = 1665732. Its totient is φ = 155520.

The previous prime is 513203. The next prime is 513239. The reversal of 513216 is 612315.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 9.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 513216.

It is an unprimeable number.

513216 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 13 ways as a sum of consecutive naturals, for example, 46651 + ... + 46661.

513216 is a Friedman number, since it can be written as 11*6^5*3*2, using all its digits and the basic arithmetic operations.

2⁵¹³²¹⁶ 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 513216, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832866).

513216 is an abundant number, since it is smaller than the sum of its proper divisors (1152516).

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

513216 is an equidigital number, since it uses as much as digits as its factorization.

513216 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41 (or 16 counting only the distinct ones).

The product of its digits is 180, while the sum is 18.

The square root of 513216 is about 716.3909547168. The cubic root of 513216 is about 80.0632832605.

Subtracting 513216 from its reverse (612315), we obtain a palindrome (99099).

It can be divided in two parts, 513 and 216, that added together give a 6-th power (729 = 3⁶).

The spelling of 513216 in words is "five hundred thirteen thousand, two hundred sixteen".