Creative numbers Problem 616

Alice plays the following game, she starts with a list of integers L and on each step she can either:

•remove two elements a and b from L and add a^{b} to L

•or conversely remove an element c from L that can be written as a^{b} , with a and b being two integers such that a,b>1 , and add both a and b to L.

For example starting from the list L={8} , Alice can remove 8 and add 2 and 3 resulting in L={2,3} in a first step. Then she can obtain L={9} in a second step.

Note that the same integer is allowed to appear multiple times in the list. An integer n>1 is said to be creative if for any integer m>1 Alice can obtain a list that contains m starting from L={n} .

Find the sum of all creative integers less than or equal to 10^{12} .