13538522400 has 432 divisors, whose sum is σ = 49406837760. Its totient is φ = 3214848000.

The previous prime is 13538522357. The next prime is 13538522401. The reversal of 13538522400 is 422583531.

13538522400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-3 number, since 3×13538522400³ (a number of 31 digits) contains 333 as substring.

It is a hoax number, since the sum of its digits (33) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (13538522401) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 11761825 + ... + 11762975.

It is an arithmetic number, because the mean of its divisors is an integer number (114367680).

Almost surely, 2^13538522400 is an apocalyptic number.

13538522400 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 13538522400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24703418880).

13538522400 is an abundant number, since it is smaller than the sum of its proper divisors (35868315360).

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

13538522400 is a wasteful number, since it uses less digits than its factorization.

13538522400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1229 (or 1203 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 33.

The spelling of 13538522400 in words is "thirteen billion, five hundred thirty-eight million, five hundred twenty-two thousand, four hundred".