105309 has 6 divisors (see below), whose sum is σ = 152126. Its totient is φ = 70200.

The previous prime is 105277. The next prime is 105319. The reversal of 105309 is 903501.

It can be written as a sum of positive squares in only one way, i.e., 99225 + 6084 = 315^2 + 78^2 .

It is not a de Polignac number, because 105309 - 2⁵ = 105277 is a prime.

It is a super-2 number, since 2×105309² = 22179970962, which contains 22 as substring.

It is a Duffinian number.

It is a Curzon number.

It is a junction number, because it is equal to n+sod(n) for n = 105291 and 105300.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105319) 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 5 ways as a sum of consecutive naturals, for example, 5842 + ... + 5859.

2¹⁰⁵³⁰⁹ is an apocalyptic number.

It is an amenable number.

105309 is a deficient number, since it is larger than the sum of its proper divisors (46817).

105309 is a wasteful number, since it uses less digits than its factorization.

105309 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11707 (or 11704 counting only the distinct ones).

The product of its (nonzero) digits is 135, while the sum is 18.

The square root of 105309 is about 324.5134820004. The cubic root of 105309 is about 47.2231728118.

It can be divided in two parts, 105 and 309, that added together give a palindrome (414).

The spelling of 105309 in words is "one hundred five thousand, three hundred nine".