138917824657920 has 5400 divisors, whose sum is σ = 673586500525092. Its totient is φ = 27259406254080.

The previous prime is 138917824657903. The next prime is 138917824657949. The reversal of 138917824657920 is 29756428719831.

138917824657920 is a `hidden beast` number, since 1 + 3 + 8 + 9 + 1 + 7 + 8 + 2 + 46 + 579 + 2 + 0 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 115439380809984 + 23478443847936 = 10744272^2 + 4845456^2 .

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

It is an unprimeable number.

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 539 ways as a sum of consecutive naturals, for example, 443826915684 + ... + 443826915996.

It is a 2-persistent number, because it is pandigital, and so is 2⋅138917824657920 = 277835649315840, but 3⋅138917824657920 = 416753473973760 is not.

Almost surely, 2^{138917824657920} is an apocalyptic number.

138917824657920 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 138917824657920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (336793250262546).

138917824657920 is an abundant number, since it is smaller than the sum of its proper divisors (534668675867172).

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

138917824657920 is a wasteful number, since it uses less digits than its factorization.

138917824657920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 422 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 365783040, while the sum is 72.

The spelling of 138917824657920 in words is "one hundred thirty-eight trillion, nine hundred seventeen billion, eight hundred twenty-four million, six hundred fifty-seven thousand, nine hundred twenty".