82321920 has 200 divisors, whose sum is σ = 295593804. Its totient is φ = 21897216.

The previous prime is 82321913. The next prime is 82321937. The reversal of 82321920 is 2912328.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 82301184 + 20736 = 9072^2 + 144^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

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 19 ways as a sum of consecutive naturals, for example, 207162 + ... + 207558.

Almost surely, 2^82321920 is an apocalyptic number.

82321920 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82321920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (147796902).

82321920 is an abundant number, since it is smaller than the sum of its proper divisors (213271884).

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

82321920 is an equidigital number, since it uses as much as digits as its factorization.

82321920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 432 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 82321920 is about 9073.1427851655. The cubic root of 82321920 is about 435.0159328290.

The spelling of 82321920 in words is "eighty-two million, three hundred twenty-one thousand, nine hundred twenty".