Examine a few prime numbers to detect the trend. Say k = 3. If S is the sum of all the positive divisors of 3, then S = 1 + 3 = 4. Notice that this is equal to k + 1, or 3 + 1.dunnec3 wrote:If k is an integer greater than 1, and S is the sum of all positive divisors of k, is S > k + 1 ?
I can't see how you can rephrase 'Is S > k + 1 ?' to 'Is k not prime ?' Can anyone help me out?
Say k = 5. If S is the sum of all positive divisors of 5, then S = 1 + 5 = 6. Again, S is equal to k + 1, or 5 + 1.
This makes sense. The only factors of a prime number are itself and 1. Therefore, if k is a prime number, the only factors of k will be 1 and k. The sum of all the factors would be 1 + k. If, by definition, the sum of the factors of a prime number 'k' is equal to k + 1, then any number whose sum is something other than k + 1 must be a non-prime number.
