A075372 Smallest squarefree number not occurring earlier such that the every partial sum is squarefree.

1, 2, 3, 5, 6, 13, 7, 10, 11, 15, 14, 19, 17, 22, 21, 29, 23, 31, 33, 35, 30, 26, 34, 38, 37, 39, 41, 47, 42, 43, 51, 46, 58, 53, 55, 61, 59, 62, 66, 57, 65, 67, 69, 70, 73, 71, 74, 78, 77, 79, 82, 86, 85, 83, 89, 87, 93, 91, 97, 101, 94, 106, 102, 105, 103, 109, 95, 113, 107