13688640 has 252 divisors, whose sum is σ = 55334916. Its totient is φ = 3096576.

The previous prime is 13688627. The next prime is 13688641. The reversal of 13688640 is 4688631.

It is a happy number.

13688640 is a `hidden beast` number, since 1 + 3 + 6 + 8 + 8 + 640 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 5531904 + 8156736 = 2352^2 + 2856^2 .

It is a tau number, because it is divible by the number of its divisors (252).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 13688595 and 13688604.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13688641) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 141072 + ... + 141168.

It is an arithmetic number, because the mean of its divisors is an integer number (219583).

Almost surely, 2^13688640 is an apocalyptic number.

13688640 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 13688640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (27667458).

13688640 is an abundant number, since it is smaller than the sum of its proper divisors (41646276).

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

13688640 is a wasteful number, since it uses less digits than its factorization.

13688640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 134 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 13688640 is about 3699.8162116516. The cubic root of 13688640 is about 239.2140959542.

Subtracting from 13688640 its reverse (4688631), we obtain a palindrome (9000009).

The spelling of 13688640 in words is "thirteen million, six hundred eighty-eight thousand, six hundred forty".