392768000 has 240 divisors, whose sum is σ = 1094454504. Its totient is φ = 140083200.

The previous prime is 392767979. The next prime is 392768021. The reversal of 392768000 is 867293.

It is an interprime number because it is at equal distance from previous prime (392767979) and next prime (392768021).

It can be written as a sum of positive squares in 4 ways, for example, as 170877184 + 221890816 = 13072^2 + 14896^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 20671991 + ... + 20672009.

Almost surely, 2^392768000 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 392768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (547227252).

392768000 is an abundant number, since it is smaller than the sum of its proper divisors (701686504).

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

392768000 is an equidigital number, since it uses as much as digits as its factorization.

392768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 43 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 35.

The square root of 392768000 is about 19818.3753118161. The cubic root of 392768000 is about 732.3387803467.

The spelling of 392768000 in words is "three hundred ninety-two million, seven hundred sixty-eight thousand".