A081001 n is in the sequence if and only if it does not rank among the top n positive integers in centrality (cf. A080997 for fuller explanation of this concept).

5, 7, 9, 11, 13, 17, 19, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 116, 118, 119