13057 has 4 divisors (see below), whose sum is σ = 14256. Its totient is φ = 11860.

The previous prime is 13049. The next prime is 13063. The reversal of 13057 is 75031.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.

It is a cyclic number.

It is not a de Polignac number, because 13057 - 2³ = 13049 is a prime.

13057 is a lucky number.

It is a self number, because there is not a number n which added to its sum of digits gives 13057.

It is not an unprimeable number, because it can be changed into a prime (13007) 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 3 ways as a sum of consecutive naturals, for example, 583 + ... + 604.

It is an arithmetic number, because the mean of its divisors is an integer number (3564).

It is a Proth number, since it is equal to 51 ⋅ 2⁸ + 1 and 51 < 2⁸.

2¹³⁰⁵⁷ is an apocalyptic number.

It is an amenable number.

13057 is a deficient number, since it is larger than the sum of its proper divisors (1199).

13057 is a wasteful number, since it uses less digits than its factorization.

13057 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1198.

The product of its (nonzero) digits is 105, while the sum is 16.

The square root of 13057 is about 114.2672306482. The cubic root of 13057 is about 23.5476624333.

Subtracting from 13057 its sum of digits (16), we obtain a triangular number (13041 = T₁₆₁).

Adding to 13057 its reverse (75031), we get a palindrome (88088).

The spelling of 13057 in words is "thirteen thousand, fifty-seven".