137746583638272 has 1728 divisors, whose sum is σ = 529809038438400. Its totient is φ = 35082007511040.

The previous prime is 137746583638247. The next prime is 137746583638331. The reversal of 137746583638272 is 272836385647731.

137746583638272 is a `hidden beast` number, since 1 + 3 + 7 + 7 + 4 + 6 + 583 + 6 + 38 + 2 + 7 + 2 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a self number, because there is not a number n which added to its sum of digits gives 137746583638272.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 37522902997 + ... + 37522906667.

It is an arithmetic number, because the mean of its divisors is an integer number (306602452800).

Almost surely, 2^{137746583638272} is an apocalyptic number.

137746583638272 is a gapful number since it is divisible by the number (12) 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 137746583638272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (264904519219200).

137746583638272 is an abundant number, since it is smaller than the sum of its proper divisors (392062454800128).

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

137746583638272 is an frugal number, since it uses more digits than its factorization.

137746583638272 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3767 (or 3719 counting only the distinct ones).

The product of its digits is 1706987520, while the sum is 72.

The spelling of 137746583638272 in words is "one hundred thirty-seven trillion, seven hundred forty-six billion, five hundred eighty-three million, six hundred thirty-eight thousand, two hundred seventy-two".