A081870 a(1)=1, a(n)=2*a(n-1)+1 if that number is not squarefree, a(n)=a(n-1)+1 otherwise.

1, 2, 3, 4, 9, 10, 11, 12, 25, 26, 27, 28, 29, 30, 31, 63, 64, 65, 66, 67, 135, 136, 137, 275, 276, 277, 278, 279, 280, 281, 282, 283, 567, 568, 569, 570, 571, 1143, 1144, 1145, 1146, 1147, 2295, 2296, 2297, 2298, 2299, 4599, 4600, 4601, 4602, 4603, 9207, 9208