137309 has 8 divisors (see below), whose sum is σ = 149688. Its totient is φ = 125440.

The previous prime is 137303. The next prime is 137321. The reversal of 137309 is 903731.

It can be written as a sum of positive squares in 4 ways, for example, as 41209 + 96100 = 203^2 + 310^2 .

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 137309 - 2¹² = 133213 is a prime.

It is a super-2 number, since 2×137309² = 37707522962, which contains 22 as substring.

It is a Duffinian number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137303) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 599 + ... + 795.

It is an arithmetic number, because the mean of its divisors is an integer number (18711).

2¹³⁷³⁰⁹ is an apocalyptic number.

It is an amenable number.

137309 is a deficient number, since it is larger than the sum of its proper divisors (12379).

137309 is a wasteful number, since it uses less digits than its factorization.

137309 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 255.

The product of its (nonzero) digits is 567, while the sum is 23.

The square root of 137309 is about 370.5522905070. The cubic root of 137309 is about 51.5900958496.

The spelling of 137309 in words is "one hundred thirty-seven thousand, three hundred nine".