137820 has 24 divisors (see below), whose sum is σ = 386064. Its totient is φ = 36736.

The previous prime is 137803. The next prime is 137827. The reversal of 137820 is 28731.

137820 = T₁₆₁ + T₁₆₂ + ... + T₁₇₀.

137820 = 3² + 4² + ... + 74².

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 137820.

It is not an unprimeable number, because it can be changed into a prime (137827) by changing a digit.

137820 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1089 + ... + 1208.

It is an arithmetic number, because the mean of its divisors is an integer number (16086).

2¹³⁷⁸²⁰ is an apocalyptic number.

137820 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

137820 is an abundant number, since it is smaller than the sum of its proper divisors (248244).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

137820 is a wasteful number, since it uses less digits than its factorization.

137820 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2309 (or 2307 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 21.

The square root of 137820 is about 371.2411615110. The cubic root of 137820 is about 51.6540147076.

The spelling of 137820 in words is "one hundred thirty-seven thousand, eight hundred twenty".