I have an intuition that Average of twin prime pairs is always Abundant number except for 4 and 6. 
For example:


12 < 1+2+3+4+6=16


18 < 1+2+3+6+9=21


...


But I can't prove this. Could you give me any good idea?




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2010-08-22
I think that Any prime is a factor of average of twin prime pair. 
Do you agree with me?



Average of twin prime pairs is Abundant number, except for 4 and 6. Any prime is a factor of average of twin prime pair
Prove the sum is always a multiple of 6, then prove that multiples of 6 are abundant. 


