Puzzle: sum freedom

(this is a reprise of a previous post)

Revised to yield a unique answer!

Sorry to all who already dug in

Three perfectly logical prisoners are seated facing each other, with hats on their heads. Each hat has a counting number {1, 2, 3, 4, …} on it, and each prisoner can see the hat of the other two prisoners, but not his own.

The warden says, “I will set free the man who can tell me his own number, but execute any man guessing incorrectly.”

They look back at him in stunned silence.

“OK, a hint. One of your numbers is the sum of the two. Alan?”
— “I don’t know my number.”
“Bert?”
— “I don’t know my number.”
“Graham?”
— “I don’t know my number.”
“Alan?”
— “I still don’t know my number.”
“Bert?”
— “My number is 78 26.″

And he went free. What were Alan and Graham’s numbers? (And how did you discover this?)

Spoiler treatment: (Please use the comments section for questions, clarifications, comments) (Please post answers here, instead).