a(n) = a(n-1) + a(n-2) + gcd(a(n-1), n), a(1) = a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =13a(5) =19a(6) =33a(7) =53a(8) =87a(9) =141a(10) =229a(11) =371a(12) =601a(13) =973a(14) =1575a(15) =2549a(16) =4125a(17) =6677a(18) =10803a(19) =17481a(20) =28287a(21) =45769a(22) =74057a(23) =119827a(24) =193885a(25) =313713a(26) =507625a(27) =821339a(28) =1328965a(29) =2150309