has 5 divisors: 1, 3, 9, 27, 81
Sum of divisors:
Are there any other primes such that the sum of all positive integer divisors of is equal to a square of an integer?
If is a prime, then the sum of all positive integer divisors of equals
where is a positive integer.
then we have obviously
and it follows that we must have
If fact, for we obtain
Thus, there exists only one prime , namely .