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

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =9a(5) =10a(6) =11a(7) =12a(8) =25a(9) =26a(10) =27a(11) =28a(12) =29a(13) =30a(14) =31a(15) =63a(16) =64a(17) =65a(18) =66a(19) =67a(20) =135a(21) =136a(22) =137a(23) =275a(24) =276a(25) =277a(26) =278a(27) =279a(28) =280a(29) =281