821288 has 32 divisors (see below), whose sum is σ = 1701000. Its totient is φ = 369408.

The previous prime is 821281. The next prime is 821291. The reversal of 821288 is 882128.

It can be written as a sum of positive squares in 4 ways, for example, as 487204 + 334084 = 698^2 + 578^2 .

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

It is a self number, because there is not a number n which added to its sum of digits gives 821288.

It is not an unprimeable number, because it can be changed into a prime (821281) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 5438 + ... + 5586.

2⁸²¹²⁸⁸ 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 821288, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (850500).

821288 is an abundant number, since it is smaller than the sum of its proper divisors (879712).

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

821288 is a wasteful number, since it uses less digits than its factorization.

821288 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 221 (or 217 counting only the distinct ones).

The product of its digits is 2048, while the sum is 29.

The square root of 821288 is about 906.2494137929. The cubic root of 821288 is about 93.6479969094.

The spelling of 821288 in words is "eight hundred twenty-one thousand, two hundred eighty-eight".