A121644 Slowest increasing sequence with squarefree cumulative sums.

1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 41, 43, 44, 45, 48, 49, 50, 52, 53, 59, 61, 63, 64, 65, 67, 68, 69, 72, 73, 75, 77, 82, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 98, 99, 100, 101, 102, 104, 106, 108, 110, 116, 117, 119, 120, 121, 123