A088609 a(1) = 1, a(n) is the smallest squarefree number not included earlier if n is not squarefree, else n is the smallest nonsquarefree number.

1, 4, 8, 2, 9, 12, 16, 3, 5, 18, 20, 6, 24, 25, 27, 7, 28, 10, 32, 11, 36, 40, 44, 13, 14, 45, 15, 17, 48, 49, 50, 19, 52, 54, 56, 21, 60, 63, 64, 22, 68, 72, 75, 23, 26, 76, 80, 29, 30, 31, 81, 33, 84, 34, 88, 35, 90, 92, 96, 37, 98, 99, 38, 39, 100, 104, 108, 41, 112, 116