137984 has 54 divisors (see below), whose sum is σ = 349524. Its totient is φ = 53760.

The previous prime is 137983. The next prime is 137993. The reversal of 137984 is 489731.

137984 is nontrivially palindromic in base 6.

It is a Smith number, since the sum of its digits (32) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a self number, because there is not a number n which added to its sum of digits gives 137984.

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

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 12539 + ... + 12549.

2¹³⁷⁹⁸⁴ is an apocalyptic number.

137984 is a gapful number since it is divisible by the number (14) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (174762).

137984 is an abundant number, since it is smaller than the sum of its proper divisors (211540).

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

137984 is an equidigital number, since it uses as much as digits as its factorization.

137984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41 (or 20 counting only the distinct ones).

The product of its digits is 6048, while the sum is 32.

The square root of 137984 is about 371.4619765198. The cubic root of 137984 is about 51.6744952873.

Multiplying 137984 by its reverse (489731), we get a square (67575042304 = 259952²).

It can be divided in two parts, 13 and 7984, that added together give a palindrome (7997).

The spelling of 137984 in words is "one hundred thirty-seven thousand, nine hundred eighty-four".