393344 has 32 divisors (see below), whose sum is σ = 897600. Its totient is φ = 168192.

The previous prime is 393331. The next prime is 393361. The reversal of 393344 is 443393.

It is a tau number, because it is divible by the number of its divisors (32).

It is an Ulam number.

It is a d-powerful number, because it can be written as 3³ + 9⁴ + 3³ + 3¹⁰ + 4⁸ + 4⁹ .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 677 + ... + 1115.

It is an arithmetic number, because the mean of its divisors is an integer number (28050).

2³⁹³³⁴⁴ 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 393344, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (448800).

393344 is an abundant number, since it is smaller than the sum of its proper divisors (504256).

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

393344 is an equidigital number, since it uses as much as digits as its factorization.

393344 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 460 (or 448 counting only the distinct ones).

The product of its digits is 3888, while the sum is 26.

The square root of 393344 is about 627.1714279206. The cubic root of 393344 is about 73.2696600655.

It can be divided in two parts, 393 and 344, that added together give a palindrome (737).

The spelling of 393344 in words is "three hundred ninety-three thousand, three hundred forty-four".