A143691 Lexicographically smallest permutation of the natural numbers having alternating even an odd numbers of prime factors.

1, 2, 4, 3, 6, 5, 9, 7, 10, 8, 14, 11, 15, 12, 16, 13, 21, 17, 22, 18, 24, 19, 25, 20, 26, 23, 33, 27, 34, 28, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 46, 41, 49, 42, 51, 43, 54, 44, 55, 45, 56, 47, 57, 48, 58, 50, 60, 52, 62, 53, 64, 59, 65, 61, 69, 63, 74, 66, 77, 67, 81, 68