4113 has 6 divisors (see below), whose sum is σ = 5954. Its totient is φ = 2736.

The previous prime is 4111. The next prime is 4127. The reversal of 4113 is 3114.

4113 is nontrivially palindromic in base 6.

It can be written as a sum of positive squares in only one way, i.e., 3969 + 144 = 63^2 + 12^2 .

It is not a de Polignac number, because 4113 - 2¹ = 4111 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9), and also a Moran number because the ratio is a prime number: 457 = 4113 / (4 + 1 + 1 + 3).

It is a Duffinian number.

It is a plaindrome in base 12.

It is a junction number, because it is equal to n+sod(n) for n = 4095 and 4104.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4111) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 220 + ... + 237.

2⁴¹¹³ is an apocalyptic number.

It is an amenable number.

4113 is a deficient number, since it is larger than the sum of its proper divisors (1841).

4113 is a wasteful number, since it uses less digits than its factorization.

4113 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 463 (or 460 counting only the distinct ones).

The product of its digits is 12, while the sum is 9.

The square root of 4113 is about 64.1326749793. The cubic root of 4113 is about 16.0221048635.

Adding to 4113 its reverse (3114), we get a palindrome (7227).

Subtracting from 4113 its reverse (3114), we obtain a palindrome (999).

It can be divided in two parts, 411 and 3, that added together give a palindrome (414).

The spelling of 4113 in words is "four thousand, one hundred thirteen".