138528 has 72 divisors (see below), whose sum is σ = 435708. Its totient is φ = 41472.

The previous prime is 138517. The next prime is 138547. The reversal of 138528 is 825831.

138528 = 12³ + 13³ + ... + 27³.

It is a happy number.

138528 is a `hidden beast` number, since 138 + 528 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 138384 + 144 = 372^2 + 12^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an unprimeable number.

138528 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3726 + ... + 3762.

2¹³⁸⁵²⁸ is an apocalyptic number.

138528 is a gapful number since it is divisible by the number (18) 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 138528, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (217854).

138528 is an abundant number, since it is smaller than the sum of its proper divisors (297180).

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

138528 is a wasteful number, since it uses less digits than its factorization.

138528 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 55 counting only the distinct ones).

The product of its digits is 1920, while the sum is 27.

The square root of 138528 is about 372.1934980625. The cubic root of 138528 is about 51.7423148988.

It can be divided in two parts, 138 and 528, that added together give a palindrome (666).

The spelling of 138528 in words is "one hundred thirty-eight thousand, five hundred twenty-eight".