681309 has 24 divisors (see below), whose sum is σ = 1073592. Its totient is φ = 414720.

The previous prime is 681293. The next prime is 681311. The reversal of 681309 is 903186.

681309 = 60³ + 61³ + 62³.

It can be written as a sum of positive squares in 4 ways, for example, as 49284 + 632025 = 222^2 + 795^2 .

It is not a de Polignac number, because 681309 - 2⁴ = 681293 is a prime.

It is a Curzon number.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 681309.

It is not an unprimeable number, because it can be changed into a prime (681409) 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 23 ways as a sum of consecutive naturals, for example, 9297 + ... + 9369.

It is an arithmetic number, because the mean of its divisors is an integer number (44733).

2⁶⁸¹³⁰⁹ is an apocalyptic number.

It is an amenable number.

681309 is a deficient number, since it is larger than the sum of its proper divisors (392283).

681309 is a wasteful number, since it uses less digits than its factorization.

681309 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 157 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 681309 is about 825.4144413566. The cubic root of 681309 is about 87.9929832560.

It can be divided in two parts, 681 and 309, that added together give a triangular number (990 = T₄₄).

The spelling of 681309 in words is "six hundred eighty-one thousand, three hundred nine".