82717000 has 64 divisors (see below), whose sum is σ = 195053040. Its totient is φ = 32832000.

The previous prime is 82716979. The next prime is 82717001. The reversal of 82717000 is 71728.

It is a happy number.

It can be written as a sum of positive squares in 8 ways, for example, as 161604 + 82555396 = 402^2 + 9086^2 .

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

It is not an unprimeable number, because it can be changed into a prime (82717001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 180772 + ... + 181228.

Almost surely, 2^82717000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82717000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (97526520).

82717000 is an abundant number, since it is smaller than the sum of its proper divisors (112336040).

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

82717000 is a wasteful number, since it uses less digits than its factorization.

82717000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 659 (or 645 counting only the distinct ones).

The product of its (nonzero) digits is 784, while the sum is 25.

The square root of 82717000 is about 9094.8886744149. Note that the first 3 decimals coincide. The cubic root of 82717000 is about 435.7107331329.

Adding to 82717000 its reverse (71728), we get a palindrome (82788728).

The spelling of 82717000 in words is "eighty-two million, seven hundred seventeen thousand".