137540 has 36 divisors (see below), whose sum is σ = 325164. Its totient is φ = 48576.

The previous prime is 137537. The next prime is 137567. The reversal of 137540 is 45731.

137540 = 10² + 11² + ... + 74².

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 33856 + 103684 = 184^2 + 322^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5969 + ... + 5991.

2¹³⁷⁵⁴⁰ is an apocalyptic number.

137540 is a gapful number since it is divisible by the number (10) 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 137540, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (162582).

137540 is an abundant number, since it is smaller than the sum of its proper divisors (187624).

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

137540 is a wasteful number, since it uses less digits than its factorization.

137540 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 68 (or 43 counting only the distinct ones).

The product of its (nonzero) digits is 420, while the sum is 20.

The square root of 137540 is about 370.8638564217. The cubic root of 137540 is about 51.6190102821.

Subtracting from 137540 its reverse (45731), we obtain a square (91809 = 303²).

The spelling of 137540 in words is "one hundred thirty-seven thousand, five hundred forty".