82971 has 16 divisors (see below), whose sum is σ = 140800. Its totient is φ = 47304.

The previous prime is 82963. The next prime is 82981. The reversal of 82971 is 17928.

It is not a de Polignac number, because 82971 - 2³ = 82963 is a prime.

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

It is a Duffinian number.

It is a plaindrome in base 14.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 82971.

It is not an unprimeable number, because it can be changed into a prime (82981) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 31 + ... + 408.

It is an arithmetic number, because the mean of its divisors is an integer number (8800).

2⁸²⁹⁷¹ is an apocalyptic number.

82971 is a deficient number, since it is larger than the sum of its proper divisors (57829).

82971 is a wasteful number, since it uses less digits than its factorization.

82971 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 455 (or 449 counting only the distinct ones).

The product of its digits is 1008, while the sum is 27.

The square root of 82971 is about 288.0468711859. The cubic root of 82971 is about 43.6156257995.

Subtracting from 82971 its sum of digits (27), we obtain a square (82944 = 288²).

It can be divided in two parts, 829 and 71, that added together give a square (900 = 30²).

The spelling of 82971 in words is "eighty-two thousand, nine hundred seventy-one".