821321 has 4 divisors (see below), whose sum is σ = 869652. Its totient is φ = 772992.

The previous prime is 821311. The next prime is 821329. The reversal of 821321 is 123128.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 436921 + 384400 = 661^2 + 620^2 .

It is a cyclic number.

It is not a de Polignac number, because 821321 - 2¹⁸ = 559177 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (17), and also a Moran number because the ratio is a prime number: 48313 = 821321 / (8 + 2 + 1 + 3 + 2 + 1).

It is a self number, because there is not a number n which added to its sum of digits gives 821321.

It is not an unprimeable number, because it can be changed into a prime (821329) 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 3 ways as a sum of consecutive naturals, for example, 24140 + ... + 24173.

It is an arithmetic number, because the mean of its divisors is an integer number (217413).

2⁸²¹³²¹ is an apocalyptic number.

It is an amenable number.

821321 is a deficient number, since it is larger than the sum of its proper divisors (48331).

821321 is a wasteful number, since it uses less digits than its factorization.

821321 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 48330.

The product of its digits is 96, while the sum is 17.

The square root of 821321 is about 906.2676205184. The cubic root of 821321 is about 93.6492511761.

Adding to 821321 its reverse (123128), we get a palindrome (944449).

The spelling of 821321 in words is "eight hundred twenty-one thousand, three hundred twenty-one".