381984 has 48 divisors (see below), whose sum is σ = 1052352. Its totient is φ = 121088.

The previous prime is 381977. The next prime is 381989. The reversal of 381984 is 489183.

381984 = 202² + 203² + ... + 210².

It is a tau number, because it is divible by the number of its divisors (48).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (381989) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2122 + ... + 2294.

It is an arithmetic number, because the mean of its divisors is an integer number (21924).

2³⁸¹⁹⁸⁴ 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 381984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (526176).

381984 is an abundant number, since it is smaller than the sum of its proper divisors (670368).

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

381984 is a wasteful number, since it uses less digits than its factorization.

381984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 209 (or 201 counting only the distinct ones).

The product of its digits is 6912, while the sum is 33.

The square root of 381984 is about 618.0485417829. The cubic root of 381984 is about 72.5574020230.

The spelling of 381984 in words is "three hundred eighty-one thousand, nine hundred eighty-four".