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?

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