137988 has 18 divisors (see below), whose sum is σ = 348894. Its totient is φ = 45984.

The previous prime is 137983. The next prime is 137993. The reversal of 137988 is 889731.

It is an interprime number because it is at equal distance from previous prime (137983) and next prime (137993).

It can be written as a sum of positive squares in only one way, i.e., 101124 + 36864 = 318^2 + 192^2 .

It is a tau number, because it is divible by the number of its divisors (18).

It is a Harshad number since it is a multiple of its sum of digits (36), and also a Moran number because the ratio is a prime number: 3833 = 137988 / (1 + 3 + 7 + 9 + 8 + 8).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 137988.

It is not an unprimeable number, because it can be changed into a prime (137983) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1881 + ... + 1952.

It is an arithmetic number, because the mean of its divisors is an integer number (19383).

2¹³⁷⁹⁸⁸ is an apocalyptic number.

137988 is a gapful number since it is divisible by the number (18) formed by its first and last digit.

It is an amenable number.

137988 is an abundant number, since it is smaller than the sum of its proper divisors (210906).

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

137988 is a wasteful number, since it uses less digits than its factorization.

137988 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3843 (or 3838 counting only the distinct ones).

The product of its digits is 12096, while the sum is 36.

The square root of 137988 is about 371.4673606119. The cubic root of 137988 is about 51.6749946109.

It can be divided in two parts, 13 and 7988, that added together give a triangular number (8001 = T₁₂₆).

The spelling of 137988 in words is "one hundred thirty-seven thousand, nine hundred eighty-eight".