512082000 has 400 divisors, whose sum is σ = 1931014800. Its totient is φ = 130636800.

The previous prime is 512081993. The next prime is 512082023. The reversal of 512082000 is 280215.

It can be written as a sum of positive squares in 8 ways, for example, as 114318864 + 397763136 = 10692^2 + 19944^2 .

It is a tau number, because it is divible by the number of its divisors (400).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 4697946 + ... + 4698054.

It is an arithmetic number, because the mean of its divisors is an integer number (4827537).

Almost surely, 2^512082000 is an apocalyptic number.

512082000 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 512082000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (965507400).

512082000 is an abundant number, since it is smaller than the sum of its proper divisors (1418932800).

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

512082000 is a wasteful number, since it uses less digits than its factorization.

512082000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 173 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 512082000 is about 22629.2288865529. The cubic root of 512082000 is about 800.0427060535.

The spelling of 512082000 in words is "five hundred twelve million, eighty-two thousand".