137193341395968 has 2112 divisors, whose sum is σ = 508153451000832. Its totient is φ = 35006667816960.

The previous prime is 137193341395907. The next prime is 137193341395991. The reversal of 137193341395968 is 869593143391731.

137193341395968 is a `hidden beast` number, since 1 + 3 + 7 + 1 + 9 + 33 + 413 + 95 + 96 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (2112).

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

It is a junction number, because it is equal to n+sod(n) for n = 137193341395896 and 137193341395905.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 118988153280 + ... + 118988154432.

Almost surely, 2^{137193341395968} is an apocalyptic number.

137193341395968 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 137193341395968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (254076725500416).

137193341395968 is an abundant number, since it is smaller than the sum of its proper divisors (370960109604864).

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

137193341395968 is a wasteful number, since it uses less digits than its factorization.

137193341395968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1380 (or 1359 counting only the distinct ones).

The product of its digits is 396809280, while the sum is 72.

The spelling of 137193341395968 in words is "one hundred thirty-seven trillion, one hundred ninety-three billion, three hundred forty-one million, three hundred ninety-five thousand, nine hundred sixty-eight".