a(n) = M(2^n), where M(n) is Mertens's function, A002321.

Terms

a(0) =1a(1) =0a(2) =-1a(3) =-2a(4) =-1a(5) =-4a(6) =-1a(7) =-2a(8) =-1a(9) =-4a(10) =-4a(11) =7a(12) =-19a(13) =22a(14) =-32a(15) =26a(16) =14a(17) =-20a(18) =24a(19) =-125a(20) =257a(21) =-362a(22) =228a(23) =-10a(24) =211a(25) =-1042a(26) =329a(27) =330a(28) =-1703a(29) =6222