13590 has 24 divisors (see below), whose sum is σ = 35568. Its totient is φ = 3600.

The previous prime is 13577. The next prime is 13591. The reversal of 13590 is 9531.

13590 is digitally balanced in base 2 and base 6, because in such bases it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (18).

13590 is strictly pandigital in base 6.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13591) by changing a digit.

13590 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 11 ways as a sum of consecutive naturals, for example, 15 + ... + 165.

It is an arithmetic number, because the mean of its divisors is an integer number (1482).

2¹³⁵⁹⁰ is an apocalyptic number.

13590 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is a practical number, because each smaller number is the sum of distinct divisors of 13590, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17784).

13590 is an abundant number, since it is smaller than the sum of its proper divisors (21978).

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

13590 is a wasteful number, since it uses less digits than its factorization.

13590 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 164 (or 161 counting only the distinct ones).

The product of its (nonzero) digits is 135, while the sum is 18.

The square root of 13590 is about 116.5761553664. The cubic root of 13590 is about 23.8638119962.

It can be divided in two parts, 135 and 90, that added together give a square (225 = 15²).

The spelling of 13590 in words is "thirteen thousand, five hundred ninety".