137138400 has 288 divisors, whose sum is σ = 567463680. Its totient is φ = 31311360.

The previous prime is 137138387. The next prime is 137138411. The reversal of 137138400 is 4831731.

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

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 150747 + ... + 151653.

It is an arithmetic number, because the mean of its divisors is an integer number (1970360).

Almost surely, 2^137138400 is an apocalyptic number.

137138400 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 137138400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (283731840).

137138400 is an abundant number, since it is smaller than the sum of its proper divisors (430325280).

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

137138400 is a wasteful number, since it uses less digits than its factorization.

137138400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 943 (or 924 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 137138400 is about 11710.6105733220. The cubic root of 137138400 is about 515.6872090232.

The spelling of 137138400 in words is "one hundred thirty-seven million, one hundred thirty-eight thousand, four hundred".