137613 has 8 divisors (see below), whose sum is σ = 209728. Its totient is φ = 78624.

The previous prime is 137597. The next prime is 137623. The reversal of 137613 is 316731.

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

It is not a de Polignac number, because 137613 - 2⁴ = 137597 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (21), and also a Moran number because the ratio is a prime number: 6553 = 137613 / (1 + 3 + 7 + 6 + 1 + 3).

It is a d-powerful number, because it can be written as 1 + 3⁵ + 6² + 7⁶ + 1 + 3⁹ .

It is a Duffinian number.

It is a Curzon number.

It is a plaindrome in base 12.

It is a nialpdrome in base 11.

It is a self number, because there is not a number n which added to its sum of digits gives 137613.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137623) 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, 3256 + ... + 3297.

It is an arithmetic number, because the mean of its divisors is an integer number (26216).

2¹³⁷⁶¹³ is an apocalyptic number.

It is an amenable number.

137613 is a deficient number, since it is larger than the sum of its proper divisors (72115).

137613 is an equidigital number, since it uses as much as digits as its factorization.

137613 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6563.

The product of its digits is 378, while the sum is 21.

The square root of 137613 is about 370.9622622316. The cubic root of 137613 is about 51.6281410108.

It can be divided in two parts, 13 and 7613, that added together give a triangular number (7626 = T₁₂₃).

The spelling of 137613 in words is "one hundred thirty-seven thousand, six hundred thirteen".