A number is squareful, also called nonsquarefree, if it contains at least one square in its prime factorization. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS A013929). The greatest multiple prime factors for the squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, ... (OEIS A046028). The least multiple prime factors for squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2, ... (OEIS A046027).

No squareful Fibonacci numbers  are known with  prime.

The sequence of smallest terms in the first run of (at least)  consecutive squareful integers for , 2, ... is 4, 8, 48, 242, 844, 22020, 217070, ... (OEIS A045882).

REFERENCES:

Sloane, N. J. A. Sequences A013929, A045882, A046027, and A046028 in "The On-Line Encyclopedia of Integer Sequences."