137114031640320 has 5184 divisors, whose sum is σ = 641662445039616. Its totient is φ = 27811216097280.

The previous prime is 137114031640307. The next prime is 137114031640357. The reversal of 137114031640320 is 23046130411731.

137114031640320 is a `hidden beast` number, since 1 + 3 + 7 + 1 + 1 + 4 + 0 + 3 + 1 + 640 + 3 + 2 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (5184).

It is a super-3 number, since 3×137114031640320³ (a number of 43 digits) contains 333 as substring.

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 polite number, since it can be written in 575 ways as a sum of consecutive naturals, for example, 345375394362 + ... + 345375394758.

It is an arithmetic number, because the mean of its divisors is an integer number (123777477824).

Almost surely, 2^{137114031640320} is an apocalyptic number.

137114031640320 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 137114031640320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (320831222519808).

137114031640320 is an abundant number, since it is smaller than the sum of its proper divisors (504548413399296).

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

137114031640320 is a wasteful number, since it uses less digits than its factorization.

137114031640320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 538 (or 505 counting only the distinct ones).

The product of its (nonzero) digits is 36288, while the sum is 36.

The spelling of 137114031640320 in words is "one hundred thirty-seven trillion, one hundred fourteen billion, thirty-one million, six hundred forty thousand, three hundred twenty".