I am tempted to submit a sequence as follows: "Numbers that are the sum of 2 nonnegative squares and not perfect powers." 2, 5, 10, 13, 17, 18, 20, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, ... Does that seem to be a good idea?