513586920 has 384 divisors, whose sum is σ = 2010193920. Its totient is φ = 102643200.

The previous prime is 513586873. The next prime is 513586933. The reversal of 513586920 is 29685315.

It is a super-3 number, since 3×513586920³ (a number of 27 digits) contains 333 as substring.

It is a Smith number, since the sum of its digits (39) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 3150759 + ... + 3150921.

It is an arithmetic number, because the mean of its divisors is an integer number (5234880).

Almost surely, 2^513586920 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 513586920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1005096960).

513586920 is an abundant number, since it is smaller than the sum of its proper divisors (1496607000).

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

513586920 is a wasteful number, since it uses less digits than its factorization.

513586920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 237 (or 222 counting only the distinct ones).

The product of its (nonzero) digits is 64800, while the sum is 39.

The square root of 513586920 is about 22662.4561775638. The cubic root of 513586920 is about 800.8256683798.

The spelling of 513586920 in words is "five hundred thirteen million, five hundred eighty-six thousand, nine hundred twenty".