813984 has 48 divisors (see below), whose sum is σ = 2187360. Its totient is φ = 264960.

The previous prime is 813971. The next prime is 813991. The reversal of 813984 is 489318.

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

It is a Smith number, since the sum of its digits (33) coincides with the sum of the digits of its prime factors.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 813984.

It is an unprimeable number.

813984 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 7 ways as a sum of consecutive naturals, for example, 5787 + ... + 5925.

It is an arithmetic number, because the mean of its divisors is an integer number (45570).

2⁸¹³⁹⁸⁴ 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 813984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1093680).

813984 is an abundant number, since it is smaller than the sum of its proper divisors (1373376).

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

813984 is a wasteful number, since it uses less digits than its factorization.

813984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 213 (or 205 counting only the distinct ones).

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

The square root of 813984 is about 902.2106184257. The cubic root of 813984 is about 93.3695551019.

The spelling of 813984 in words is "eight hundred thirteen thousand, nine hundred eighty-four".