513729216 has 588 divisors, whose sum is σ = 2067728656. Its totient is φ = 123171840.

The previous prime is 513729199. The next prime is 513729217. The reversal of 513729216 is 612927315.

It is a Harshad number since it is a multiple of its sum of digits (36).

Its product of digits (22680) is a multiple of the sum of its prime divisors (36).

It is not an unprimeable number, because it can be changed into a prime (513729217) by changing a digit.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 39517626 + ... + 39517638.

Almost surely, 2^513729216 is an apocalyptic number.

513729216 is a gapful number since it is divisible by the number (56) 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 513729216, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1033864328).

513729216 is an abundant number, since it is smaller than the sum of its proper divisors (1553999440).

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

513729216 is a wasteful number, since it uses less digits than its factorization.

513729216 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 72 (or 36 counting only the distinct ones).

The product of its digits is 22680, while the sum is 36.

The square root of 513729216 is about 22665.5954256666. The cubic root of 513729216 is about 800.8996213060.

The spelling of 513729216 in words is "five hundred thirteen million, seven hundred twenty-nine thousand, two hundred sixteen".