Primes in this sequence are A113239. Perfect powers include: 9 = 3^2, 125 = 5^3, 1681 = 41^2, 2209 = 47^2, 25281 = 159^2 = 3^2 * 53^2. A113188-A113194 deal with difference sets of Fibonacci numbers and Lucas numbers and primes in those difference sets.