[math-fun] what is known about the squareful Fibonacci numbers?

[[ apart from the fact that any fib(n) containing a factor p^i (i>1 of course) seems to have mod(n,p)=0 ]] up to fib(258), at least one of fib(k) .. fib(k+6) is squareful. Analogously, the squareful fibs are spaced no more than 6 apart. Anyone for a counter-example? Their separations are counted as {1, 5 times}, {2, 11 times}, {3, 5}, {4, 7}, {5, 4}, {6, 27} So 6 is a ‘preferred distance’ for lowish n. Wouter