137813 has 4 divisors (see below), whose sum is σ = 148428. Its totient is φ = 127200.

The previous prime is 137803. The next prime is 137827. The reversal of 137813 is 318731.

137813 = 262² + 263².

It is a happy number.

It is a semiprime because it is the product of two primes, and also an emirpimes, since its reverse is a distinct semiprime: 318731 = 7 ⋅45533.

It can be written as a sum of positive squares in 2 ways, for example, as 69169 + 68644 = 263^2 + 262^2 .

It is a cyclic number.

It is not a de Polignac number, because 137813 - 2¹² = 133717 is a prime.

It is a Duffinian number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (137803) 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, 5288 + ... + 5313.

It is an arithmetic number, because the mean of its divisors is an integer number (37107).

2¹³⁷⁸¹³ is an apocalyptic number.

137813 is a gapful number since it is divisible by the number (13) formed by its first and last digit.

137813 is the 263-rd centered square number.

It is an amenable number.

137813 is a deficient number, since it is larger than the sum of its proper divisors (10615).

137813 is a wasteful number, since it uses less digits than its factorization.

137813 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 10614.

The product of its digits is 504, while the sum is 23.

The square root of 137813 is about 371.2317335574. The cubic root of 137813 is about 51.6531401751.

The spelling of 137813 in words is "one hundred thirty-seven thousand, eight hundred thirteen".