388416 has 84 divisors (see below), whose sum is σ = 1247648. Its totient is φ = 104448.

The previous prime is 388403. The next prime is 388459. The reversal of 388416 is 614883.

It is a happy number.

388416 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (84).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

388416 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 22840 + ... + 22856.

388416 is a Friedman number, since it can be written as 84*68^(3-1), using all its digits and the basic arithmetic operations.

2³⁸⁸⁴¹⁶ 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 388416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (623824).

388416 is an abundant number, since it is smaller than the sum of its proper divisors (859232).

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

388416 is a wasteful number, since it uses less digits than its factorization.

388416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 29 counting only the distinct ones).

The product of its digits is 4608, while the sum is 30.

The square root of 388416 is about 623.2302945140. The cubic root of 388416 is about 72.9623875796.

The spelling of 388416 in words is "three hundred eighty-eight thousand, four hundred sixteen".