13530 has 32 divisors (see below), whose sum is σ = 36288. Its totient is φ = 3200.

The previous prime is 13523. The next prime is 13537. The reversal of 13530 is 3531.

13530 = T₄₄ + T₄₅ + ... + T₅₄.

13530 = 50² + 51² + ... + 54².

It is a happy number.

13530 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

13530 is a nontrivial binomial coefficient, being equal to C(165, 2).

It is an interprime number because it is at equal distance from previous prime (13523) and next prime (13537).

13530 is strictly pandigital in base 6.

It is a Curzon number.

It is not an unprimeable number, because it can be changed into a prime (13537) by changing a digit.

13530 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 310 + ... + 350.

It is an arithmetic number, because the mean of its divisors is an integer number (1134).

2¹³⁵³⁰ is an apocalyptic number.

13530 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

13530 is the 164-th triangular number.

It is a practical number, because each smaller number is the sum of distinct divisors of 13530, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18144).

13530 is an abundant number, since it is smaller than the sum of its proper divisors (22758).

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

13530 is a wasteful number, since it uses less digits than its factorization.

13530 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62.

The product of its (nonzero) digits is 45, while the sum is 12.

The square root of 13530 is about 116.3185281888. The cubic root of 13530 is about 23.8286405201.

Subtracting from 13530 its reverse (3531), we obtain a palindrome (9999).

The spelling of 13530 in words is "thirteen thousand, five hundred thirty".