137520 has 60 divisors (see below), whose sum is σ = 464256. Its totient is φ = 36480.

The previous prime is 137519. The next prime is 137537. The reversal of 137520 is 25731.

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a d-powerful number, because it can be written as 1 + 3¹⁰ + 5⁷ + 7³ + 2 + 0 .

It is a junction number, because it is equal to n+sod(n) for n = 137493 and 137502.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 137520.

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, 625 + ... + 815.

2¹³⁷⁵²⁰ is an apocalyptic number.

137520 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 137520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (232128).

137520 is an abundant number, since it is smaller than the sum of its proper divisors (326736).

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

137520 is a wasteful number, since it uses less digits than its factorization.

137520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 210 (or 201 counting only the distinct ones).

The product of its (nonzero) digits is 210, while the sum is 18.

The square root of 137520 is about 370.8368913687. The cubic root of 137520 is about 51.6165081487.

The spelling of 137520 in words is "one hundred thirty-seven thousand, five hundred twenty".