138384000 has 288 divisors, whose sum is σ = 513520020. Its totient is φ = 35712000.

The previous prime is 138383989. The next prime is 138384017. The reversal of 138384000 is 483831.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 93547584 + 44836416 = 9672^2 + 6696^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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 35 ways as a sum of consecutive naturals, for example, 4463985 + ... + 4464015.

Almost surely, 2^138384000 is an apocalyptic number.

138384000 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 138384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (256760010).

138384000 is an abundant number, since it is smaller than the sum of its proper divisors (375136020).

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

138384000 is an equidigital number, since it uses as much as digits as its factorization.

138384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 97 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 138384000 is about 11763.6728958264. The cubic root of 138384000 is about 517.2437995289.

The spelling of 138384000 in words is "one hundred thirty-eight million, three hundred eighty-four thousand".