138101424400 has 135 divisors (see below), whose sum is σ = 352776470061. Its totient is φ = 51943557120.

The previous prime is 138101424371. The next prime is 138101424401. The reversal of 138101424400 is 4424101831.

The square root of 138101424400 is 371620.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 145636624 + 137955787776 = 12068^2 + 371424^2 .

It is a super-3 number, since 3×138101424400³ (a number of 34 digits) contains 333 as substring.

It is a hoax number, since the sum of its digits (28) coincides with the sum of the digits of its distinct prime factors.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (138101424401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 126350254 + ... + 126351346.

Almost surely, 2^138101424400 is an apocalyptic number.

138101424400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

138101424400 is the 371620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138101424400

138101424400 is an abundant number, since it is smaller than the sum of its proper divisors (214675045661).

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

138101424400 is an equidigital number, since it uses as much as digits as its factorization.

138101424400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2238 (or 1117 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 28.

The spelling of 138101424400 in words is "one hundred thirty-eight billion, one hundred one million, four hundred twenty-four thousand, four hundred".