13723129728 has 768 divisors, whose sum is σ = 52744608000. Its totient is φ = 3472035840.

The previous prime is 13723129703. The next prime is 13723129733. The reversal of 13723129728 is 82792132731.

13723129728 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 3×13723129728³ (a number of 31 digits) contains 333 as substring.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

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 95 ways as a sum of consecutive naturals, for example, 98727483 + ... + 98727621.

It is an arithmetic number, because the mean of its divisors is an integer number (68677875).

Almost surely, 2^13723129728 is an apocalyptic number.

13723129728 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 13723129728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (26372304000).

13723129728 is an abundant number, since it is smaller than the sum of its proper divisors (39021478272).

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

13723129728 is a wasteful number, since it uses less digits than its factorization.

13723129728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 240 (or 215 counting only the distinct ones).

The product of its digits is 254016, while the sum is 45.

The spelling of 13723129728 in words is "thirteen billion, seven hundred twenty-three million, one hundred twenty-nine thousand, seven hundred twenty-eight".