138504038400 has 1440 divisors, whose sum is σ = 633091979520. Its totient is φ = 29143203840.

The previous prime is 138504038381. The next prime is 138504038411. The reversal of 138504038400 is 4830405831.

138504038400 is a `hidden beast` number, since 138 + 50 + 40 + 38 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 377395017 + ... + 377395383.

It is an arithmetic number, because the mean of its divisors is an integer number (439647208).

Almost surely, 2^138504038400 is an apocalyptic number.

138504038400 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 138504038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (316545989760).

138504038400 is an abundant number, since it is smaller than the sum of its proper divisors (494587941120).

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

138504038400 is a wasteful number, since it uses less digits than its factorization.

138504038400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 431 (or 397 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The spelling of 138504038400 in words is "one hundred thirty-eight billion, five hundred four million, thirty-eight thousand, four hundred".