164001600 has 252 divisors, whose sum is σ = 666581344. Its totient is φ = 37463040.

The previous prime is 164001587. The next prime is 164001623. The reversal of 164001600 is 6100461.

164001600 is a `hidden beast` number, since 1 + 64 + 0 + 0 + 1 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (252).

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 (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 99987 + ... + 101613.

Almost surely, 2^164001600 is an apocalyptic number.

164001600 is a gapful number since it is divisible by the number (10) 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 164001600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (333290672).

164001600 is an abundant number, since it is smaller than the sum of its proper divisors (502579744).

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

164001600 is a wasteful number, since it uses less digits than its factorization.

164001600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1662 (or 1644 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 164001600 is about 12806.3109442181. The cubic root of 164001600 is about 547.3721475403.

The spelling of 164001600 in words is "one hundred sixty-four million, one thousand, six hundred".