137822128213968 has 1200 divisors, whose sum is σ = 463724599726080. Its totient is φ = 39431411712000.

The previous prime is 137822128213961. The next prime is 137822128214027. The reversal of 137822128213968 is 869312821228731.

137822128213968 is a `hidden beast` number, since 1 + 3 + 7 + 8 + 2 + 212 + 8 + 21 + 396 + 8 = 666.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137822128213961) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (29) of ones.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 41006284608 + ... + 41006287968.

Almost surely, 2^{137822128213968} is an apocalyptic number.

137822128213968 is a gapful number since it is divisible by the number (18) 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 137822128213968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (231862299863040).

137822128213968 is an abundant number, since it is smaller than the sum of its proper divisors (325902471512112).

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

137822128213968 is a wasteful number, since it uses less digits than its factorization.

137822128213968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3630 (or 3604 counting only the distinct ones).

The product of its digits is 27869184, while the sum is 63.

The spelling of 137822128213968 in words is "one hundred thirty-seven trillion, eight hundred twenty-two billion, one hundred twenty-eight million, two hundred thirteen thousand, nine hundred sixty-eight".