nonsquarefree

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 F_p are known with p prime. The sequence of smallest terms in the first run of (at least) n consecutive squareful integers for n = 1, 2, ... is 4, 8, 48, 242, 844, 22020, 217070, ... (OEIS A045882).

greatest prime factor | least prime factor | Smarandache near-to-primorial function | squarefree