105313 has 4 divisors (see below), whose sum is σ = 113428. Its totient is φ = 97200.

The previous prime is 105277. The next prime is 105319. The reversal of 105313 is 313501.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 71824 + 33489 = 268^2 + 183^2 .

It is a cyclic number.

It is not a de Polignac number, because 105313 - 2⁹ = 104801 is a prime.

It is a super-2 number, since 2×105313² = 22181655938, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (13), and also a Moran number because the ratio is a prime number: 8101 = 105313 / (1 + 0 + 5 + 3 + 1 + 3).

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 105293 and 105302.

It is not an unprimeable number, because it can be changed into a prime (105319) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 4038 + ... + 4063.

It is an arithmetic number, because the mean of its divisors is an integer number (28357).

2¹⁰⁵³¹³ is an apocalyptic number.

105313 is a gapful number since it is divisible by the number (13) formed by its first and last digit.

It is an amenable number.

105313 is a deficient number, since it is larger than the sum of its proper divisors (8115).

105313 is an equidigital number, since it uses as much as digits as its factorization.

105313 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8114.

The product of its (nonzero) digits is 45, while the sum is 13.

The square root of 105313 is about 324.5196450140. The cubic root of 105313 is about 47.2237707041.

Adding to 105313 its reverse (313501), we get a palindrome (418814).

It can be divided in two parts, 1053 and 13, that multiplied together give a square (13689 = 117²).

The spelling of 105313 in words is "one hundred five thousand, three hundred thirteen".