82386220105728 has 1440 divisors, whose sum is σ = 301993128702720. Its totient is φ = 21023026053120.

The previous prime is 82386220105723. The next prime is 82386220105747. The reversal of 82386220105728 is 82750102268328.

82386220105728 is a `hidden beast` number, since 8 + 2 + 3 + 8 + 62 + 2 + 0 + 1 + 0 + 572 + 8 = 666.

It is not an unprimeable number, because it can be changed into a prime (82386220105723) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 201433300788 + ... + 201433301196.

It is an arithmetic number, because the mean of its divisors is an integer number (209717450488).

Almost surely, 2^{82386220105728} is an apocalyptic number.

82386220105728 is a gapful number since it is divisible by the number (88) 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 82386220105728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (150996564351360).

82386220105728 is an abundant number, since it is smaller than the sum of its proper divisors (219606908596992).

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

82386220105728 is a wasteful number, since it uses less digits than its factorization.

82386220105728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 731 (or 702 counting only the distinct ones).

The product of its (nonzero) digits is 5160960, while the sum is 54.

The spelling of 82386220105728 in words is "eighty-two trillion, three hundred eighty-six billion, two hundred twenty million, one hundred five thousand, seven hundred twenty-eight".