A080823 a(n)=n for n<=4; for n>4, a(n) is the smallest integer greater than a(n-1) that shares common factors with some (i.e. at least one) but not all of previous 4 terms.

1, 2, 3, 4, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 51, 52, 55, 56, 57, 58, 62, 63, 64, 68, 69, 70, 74, 75, 76, 77, 78, 80, 81, 82, 85, 86, 87, 88, 92, 93, 94, 98, 99, 100, 104, 105, 106, 111, 112, 115, 116, 117, 118, 122