386048000 has 224 divisors, whose sum is σ = 1073414160. Its totient is φ = 137625600.

The previous prime is 386047999. The next prime is 386048009. The reversal of 386048000 is 840683.

It can be written as a sum of positive squares in 8 ways, for example, as 4096 + 386043904 = 64^2 + 19648^2 .

It is a Harshad number since it is a multiple of its sum of digits (29).

It is not an unprimeable number, because it can be changed into a prime (386048009) by changing a digit.

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, 13311986 + ... + 13312014.

Almost surely, 2^386048000 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 386048000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (536707080).

386048000 is an abundant number, since it is smaller than the sum of its proper divisors (687366160).

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

386048000 is an equidigital number, since it uses as much as digits as its factorization.

386048000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 83 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 29.

The square root of 386048000 is about 19648.1042342512. The cubic root of 386048000 is about 728.1381213597.

Adding to 386048000 its reverse (840683), we get a palindrome (386888683).

The spelling of 386048000 in words is "three hundred eighty-six million, forty-eight thousand".