164072000 has 56 divisors (see below), whose sum is σ = 406344120. Its totient is φ = 65625600.

The previous prime is 164071997. The next prime is 164072003. The reversal of 164072000 is 270461.

164072000 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (164071997) and next prime (164072003).

It can be written as a sum of positive squares in 4 ways, for example, as 21603904 + 142468096 = 4648^2 + 11936^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (164072003) by changing a digit.

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 7 ways as a sum of consecutive naturals, for example, 2255 + ... + 18254.

It is an arithmetic number, because the mean of its divisors is an integer number (7256145).

Almost surely, 2^164072000 is an apocalyptic number.

164072000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

164072000 is an abundant number, since it is smaller than the sum of its proper divisors (242272120).

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

164072000 is an equidigital number, since it uses as much as digits as its factorization.

164072000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 20536 (or 20516 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 20.

The square root of 164072000 is about 12809.0592941090. The cubic root of 164072000 is about 547.4504587409.

The spelling of 164072000 in words is "one hundred sixty-four million, seventy-two thousand".