82131200 has 108 divisors (see below), whose sum is σ = 208911108. Its totient is φ = 31948800.

The previous prime is 82131191. The next prime is 82131209. The reversal of 82131200 is 213128.

It is an interprime number because it is at equal distance from previous prime (82131191) and next prime (82131209).

It can be written as a sum of positive squares in 6 ways, for example, as 40347904 + 41783296 = 6352^2 + 6464^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82131209) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 262244 + ... + 262556.

Almost surely, 2^82131200 is an apocalyptic number.

82131200 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 82131200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104455554).

82131200 is an abundant number, since it is smaller than the sum of its proper divisors (126779908).

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

82131200 is a wasteful number, since it uses less digits than its factorization.

82131200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 380 (or 361 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 17.

The square root of 82131200 is about 9062.6265508405. The cubic root of 82131200 is about 434.6797307895.

Adding to 82131200 its reverse (213128), we get a palindrome (82344328).

It can be divided in two parts, 82 and 131200, that multiplied together give a square (10758400 = 3280²).

The spelling of 82131200 in words is "eighty-two million, one hundred thirty-one thousand, two hundred".