393045120 has 384 divisors, whose sum is σ = 1520391600. Its totient is φ = 92897280.

The previous prime is 393045119. The next prime is 393045131. The reversal of 393045120 is 21540393.

It can be written as a sum of positive squares in 8 ways, for example, as 14197824 + 378847296 = 3768^2 + 19464^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2171430 + ... + 2171610.

Almost surely, 2^393045120 is an apocalyptic number.

393045120 is a gapful number since it is divisible by the number (30) 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 393045120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (760195800).

393045120 is an abundant number, since it is smaller than the sum of its proper divisors (1127346480).

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

393045120 is a wasteful number, since it uses less digits than its factorization.

393045120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 248 (or 233 counting only the distinct ones).

The product of its (nonzero) digits is 3240, while the sum is 27.

The square root of 393045120 is about 19825.3655704000. The cubic root of 393045120 is about 732.5109753080.

The spelling of 393045120 in words is "three hundred ninety-three million, forty-five thousand, one hundred twenty".