13689 has 15 divisors (see below), whose sum is σ = 22143. Its totient is φ = 8424.

The previous prime is 13687. The next prime is 13691. The reversal of 13689 is 98631.

Multipling 13689 by its product of digits (1296), we get a square (17740944 = 4212^{2}).

It can be divided in two parts, 136 and 89, that added together give a square (225 = 15^{2}).

13689 = T_{116} + T_{117}.

The square root of 13689 is 117.

It is a perfect power (a square), and thus also a powerful number.

It is an interprime number because it is at equal distance from previous prime (13687) and next prime (13691).

It can be written as a sum of positive squares in only one way, i.e., 2025 + 11664 = 45^2 + 108^2 .

It is not a de Polignac number, because 13689 - 2^{1} = 13687 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an Ulam number.

Its product of digits (1296) is a multiple of the sum of its prime divisors (16).

It is a plaindrome in base 10 and base 16.

It is a nialpdrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (13681) by changing a digit.

It is a polite number, since it can be written in 14 ways as a sum of consecutive naturals, for example, 1047 + ... + 1059.

13689 is a Friedman number, since it can be written as (13*9)^(8-6), using all its digits and the basic arithmetic operations.

2^{13689} is an apocalyptic number.

13689 is the 117-th square number.

13689 is the 59-th centered octagonal number.

It is an amenable number.

13689 is a deficient number, since it is larger than the sum of its proper divisors (8454).

13689 is an equidigital number, since it uses as much as digits as its factorization.

13689 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 16 counting only the distinct ones).

The product of its digits is 1296, while the sum is 27.

The cubic root of 13689 is about 23.9216192981.

The spelling of 13689 in words is "thirteen thousand, six hundred eighty-nine".

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