137793321331600 has 405 divisors, whose sum is σ = 367050936389529. Its totient is φ = 49673744947200.

The previous prime is 137793321331541. The next prime is 137793321331607. The reversal of 137793321331600 is 6133123397731.

The square root of 137793321331600 is 11738540.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 60582374107024 + 77210947224576 = 7783468^2 + 8786976^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (137793321331607) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 591387645084 + ... + 591387645316.

Almost surely, 2^{137793321331600} is an apocalyptic number.

137793321331600 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

137793321331600 is the 11738540-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137793321331600

137793321331600 is an abundant number, since it is smaller than the sum of its proper divisors (229257615057929).

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

137793321331600 is an equidigital number, since it uses as much as digits as its factorization.

137793321331600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 964 (or 480 counting only the distinct ones).

The product of its (nonzero) digits is 1285956, while the sum is 49.

The spelling of 137793321331600 in words is "one hundred thirty-seven trillion, seven hundred ninety-three billion, three hundred twenty-one million, three hundred thirty-one thousand, six hundred".