82005120 has 192 divisors, whose sum is σ = 295963200. Its totient is φ = 20883456.

The previous prime is 82005107. The next prime is 82005163. The reversal of 82005120 is 2150028.

It is a tau number, because it is divible by the number of its divisors (192).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 82005093 and 82005102.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 132171 + ... + 132789.

It is an arithmetic number, because the mean of its divisors is an integer number (1541475).

Almost surely, 2^82005120 is an apocalyptic number.

82005120 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 82005120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (147981600).

82005120 is an abundant number, since it is smaller than the sum of its proper divisors (213958080).

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

82005120 is a wasteful number, since it uses less digits than its factorization.

82005120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 667 (or 652 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 82005120 is about 9055.6678384314. The cubic root of 82005120 is about 434.4571905615.

Adding to 82005120 its reverse (2150028), we get a palindrome (84155148).

The spelling of 82005120 in words is "eighty-two million, five thousand, one hundred twenty".