A squareful integer, also called nonsquarefree, is a positive integer divisible by the square of a prime. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS A013929). The greatest prime factors occurring with exponent at least two in the prime factorization of squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, ... (OEIS A046028). The least such prime factors 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).
