138516 has 48 divisors (see below), whose sum is σ = 395136. Its totient is φ = 36864.

The previous prime is 138511. The next prime is 138517. The reversal of 138516 is 615831.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 138516.

It is not an unprimeable number, because it can be changed into a prime (138511) by changing a digit.

138516 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 (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1380 + ... + 1476.

It is an arithmetic number, because the mean of its divisors is an integer number (8232).

2¹³⁸⁵¹⁶ 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 138516, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (197568).

138516 is an abundant number, since it is smaller than the sum of its proper divisors (256620).

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

138516 is a wasteful number, since it uses less digits than its factorization.

138516 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 126 counting only the distinct ones).

The product of its digits is 720, while the sum is 24.

The square root of 138516 is about 372.1773770664. The cubic root of 138516 is about 51.7408207949.

The spelling of 138516 in words is "one hundred thirty-eight thousand, five hundred sixteen".