82081600 has 126 divisors (see below), whose sum is σ = 212605874. Its totient is φ = 31180800.

The previous prime is 82081591. The next prime is 82081607. The reversal of 82081600 is 618028.

It can be written as a sum of positive squares in 9 ways, for example, as 43243776 + 38837824 = 6576^2 + 6232^2 .

It is a hoax number, since the sum of its digits (25) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82081607) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1345570 + ... + 1345630.

Almost surely, 2^82081600 is an apocalyptic number.

82081600 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 82081600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (106302937).

82081600 is an abundant number, since it is smaller than the sum of its proper divisors (130524274).

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

82081600 is a wasteful number, since it uses less digits than its factorization.

82081600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 141 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 25.

The square root of 82081600 is about 9059.8896240517. The cubic root of 82081600 is about 434.5922104308.

Adding to 82081600 its reverse (618028), we get a palindrome (82699628).

The spelling of 82081600 in words is "eighty-two million, eighty-one thousand, six hundred".