137408 has 28 divisors (see below), whose sum is σ = 289560. Its totient is φ = 64512.

The previous prime is 137399. The next prime is 137413. The reversal of 137408 is 804731.

It is a happy number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 137408.

It is an unprimeable number.

137408 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 3 ways as a sum of consecutive naturals, for example, 1160 + ... + 1272.

2¹³⁷⁴⁰⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 137408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144780).

137408 is an abundant number, since it is smaller than the sum of its proper divisors (152152).

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

137408 is a wasteful number, since it uses less digits than its factorization.

137408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 144 (or 134 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 23.

The square root of 137408 is about 370.6858508225. The cubic root of 137408 is about 51.6024917171.

It can be divided in two parts, 137 and 408, that added together give a palindrome (545).

The spelling of 137408 in words is "one hundred thirty-seven thousand, four hundred eight".