3249 has 9 divisors (see below), whose sum is σ = 4953. Its totient is φ = 2052.

The previous prime is 3229. The next prime is 3251. The reversal of 3249 is 9423.

3249 = T₅₆ + T₅₇.

The square root of 3249 is 57.

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

3249 is nontrivially palindromic in base 7.

3249 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

3249 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (9).

It is not a de Polignac number, because 3249 - 2⁵ = 3217 is a prime.

It is a nialpdrome in base 9 and base 16.

It is not an unprimeable number, because it can be changed into a prime (3209) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 162 + ... + 180.

2³²⁴⁹ is an apocalyptic number.

3249 is the 57-th square number.

3249 is the 29-th centered octagonal number.

It is an amenable number.

3249 is a deficient number, since it is larger than the sum of its proper divisors (1704).

3249 is a wasteful number, since it uses less digits than its factorization.

With its predecessor (3248) it forms a Ruth-Aaron pair, since the sum of their prime factors is the same (44).

3249 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 44 (or 22 counting only the distinct ones).

The product of its digits is 216, while the sum is 18.

The cubic root of 3249 is about 14.8109609574.

It can be divided in two parts, 324 and 9, that multiplied together give a square (2916 = 54²).

The spelling of 3249 in words is "three thousand, two hundred forty-nine".