113013 has 12 divisors (see below), whose sum is σ = 169260. Its totient is φ = 72576.

The previous prime is 113011. The next prime is 113017. The reversal of 113013 is 310311.

It can be written as a sum of positive squares in 2 ways, for example, as 33489 + 79524 = 183^2 + 282^2 .

It is not a de Polignac number, because 113013 - 2¹ = 113011 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a Curzon number.

It is a plaindrome in base 11.

It is a junction number, because it is equal to n+sod(n) for n = 112986 and 113004.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (113011) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 45 + ... + 477.

It is an arithmetic number, because the mean of its divisors is an integer number (14105).

2¹¹³⁰¹³ is an apocalyptic number.

It is an amenable number.

113013 is a deficient number, since it is larger than the sum of its proper divisors (56247).

113013 is a wasteful number, since it uses less digits than its factorization.

113013 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 468 (or 465 counting only the distinct ones).

The product of its (nonzero) digits is 9, while the sum is 9.

The square root of 113013 is about 336.1740620571. The cubic root of 113013 is about 48.3477351719.

Adding to 113013 its reverse (310311), we get a palindrome (423324).

The spelling of 113013 in words is "one hundred thirteen thousand, thirteen".