A013933 Sum of first a(n) non-squarefrees is non-squarefree.

1, 2, 5, 9, 15, 16, 17, 24, 25, 26, 27, 29, 31, 32, 33, 35, 37, 40, 41, 43, 44, 45, 49, 50, 51, 58, 59, 61, 64, 66, 69, 72, 76, 77, 79, 80, 81, 82, 83, 84, 85, 88, 89, 93, 94, 95, 99, 101, 102, 103, 104, 108, 109, 110, 111, 116, 117, 118, 120, 133, 134, 137, 142, 146, 147, 149