13540 has 12 divisors (see below), whose sum is σ = 28476. Its totient is φ = 5408.

The previous prime is 13537. The next prime is 13553. The reversal of 13540 is 4531.

13540 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 10404 + 3136 = 102^2 + 56^2 .

It is a nialpdrome in base 7.

It is a self number, because there is not a number n which added to its sum of digits gives 13540.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 319 + ... + 358.

It is an arithmetic number, because the mean of its divisors is an integer number (2373).

2¹³⁵⁴⁰ is an apocalyptic number.

13540 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

13540 is an abundant number, since it is smaller than the sum of its proper divisors (14936).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14238).

13540 is a wasteful number, since it uses less digits than its factorization.

13540 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 686 (or 684 counting only the distinct ones).

The product of its (nonzero) digits is 60, while the sum is 13.

The square root of 13540 is about 116.3615056623. The cubic root of 13540 is about 23.8345096436.

Subtracting from 13540 its reverse (4531), we obtain a palindrome (9009).

The spelling of 13540 in words is "thirteen thousand, five hundred forty".