18513 has 18 divisors (see below), whose sum is σ = 31122. Its totient is φ = 10560.

The previous prime is 18503. The next prime is 18517. The reversal of 18513 is 31581.

18513 = 12² + 13² + ... + 38².

It is a happy number.

18513 is digitally balanced in base 3, 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 only one way, i.e., 17424 + 1089 = 132^2 + 33^2 .

It is not a de Polignac number, because 18513 - 2⁵ = 18481 is a prime.

It is a Smith number, since the sum of its digits (18) coincides with the sum of the digits of its prime factors.

It is an Ulam number.

18513 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (18517) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1081 + ... + 1097.

It is an arithmetic number, because the mean of its divisors is an integer number (1729).

2¹⁸⁵¹³ is an apocalyptic number.

It is an amenable number.

18513 is a deficient number, since it is larger than the sum of its proper divisors (12609).

18513 is a wasteful number, since it uses less digits than its factorization.

18513 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 45 (or 31 counting only the distinct ones).

The product of its digits is 120, while the sum is 18.

The square root of 18513 is about 136.0624856454. The cubic root of 18513 is about 26.4540559077.

The spelling of 18513 in words is "eighteen thousand, five hundred thirteen".