393216 has 36 divisors (see below), whose sum is σ = 1048572. Its totient is φ = 131072.

The previous prime is 393209. The next prime is 393241. The reversal of 393216 is 612393.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (2!)¹⁴.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nialpdrome in base 2 and base 16.

It is a zygodrome in base 2.

It is a congruent number.

It is an unprimeable number.

393216 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

In principle, a polygon with 393216 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 131071 + 131072 + 131073.

It is an arithmetic number, because the mean of its divisors is an integer number (29127).

393216 is a Friedman number, since it can be written as 12/(3/96)^3, using all its digits and the basic arithmetic operations.

2³⁹³²¹⁶ 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 393216, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (524286).

393216 is an abundant number, since it is smaller than the sum of its proper divisors (655356).

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

393216 is an frugal number, since it uses more digits than its factorization.

393216 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37 (or 5 counting only the distinct ones).

The product of its digits is 972, while the sum is 24.

The square root of 393216 is about 627.0693741525. The cubic root of 393216 is about 73.2617115234.

Multiplying 393216 by its sum of digits (24), we get a square (9437184 = 3072²).

393216 divided by its sum of digits (24) gives a 14-th power (16384 = 2¹⁴).

The spelling of 393216 in words is "three hundred ninety-three thousand, two hundred sixteen".