138312000 has 336 divisors, whose sum is σ = 528504912. Its totient is φ = 34406400.

The previous prime is 138311993. The next prime is 138312007. The reversal of 138312000 is 213831.

It is an interprime number because it is at equal distance from previous prime (138311993) and next prime (138312007).

It can be written as a sum of positive squares in 8 ways, for example, as 68956416 + 69355584 = 8304^2 + 8328^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138312007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1223944 + ... + 1224056.

Almost surely, 2^138312000 is an apocalyptic number.

138312000 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 138312000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (264252456).

138312000 is an abundant number, since it is smaller than the sum of its proper divisors (390192912).

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

138312000 is a wasteful number, since it uses less digits than its factorization.

138312000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 163 (or 140 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 138312000 is about 11760.6122289616. The cubic root of 138312000 is about 517.1540781395.

Adding to 138312000 its reverse (213831), we get a palindrome (138525831).

The spelling of 138312000 in words is "one hundred thirty-eight million, three hundred twelve thousand".