513085000 has 80 divisors (see below), whose sum is σ = 1216719900. Its totient is φ = 202752000.

The previous prime is 513084991. The next prime is 513085003. The reversal of 513085000 is 580315.

It can be written as a sum of positive squares in 10 ways, for example, as 43322724 + 469762276 = 6582^2 + 21674^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513085003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 444424 + ... + 445576.

Almost surely, 2^513085000 is an apocalyptic number.

513085000 is a gapful number since it is divisible by the number (50) 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 513085000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (608359950).

513085000 is an abundant number, since it is smaller than the sum of its proper divisors (703634900).

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

513085000 is a wasteful number, since it uses less digits than its factorization.

513085000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1268 (or 1249 counting only the distinct ones).

The product of its (nonzero) digits is 600, while the sum is 22.

The square root of 513085000 is about 22651.3796489309. The cubic root of 513085000 is about 800.5647054576.

The spelling of 513085000 in words is "five hundred thirteen million, eighty-five thousand".