a(n) = Sum_{k=1..n} 4^(gcd(k, n) - 1).

Terms

a(0) =1a(1) =5a(2) =18a(3) =70a(4) =260a(5) =1050a(6) =4102a(7) =16460a(8) =65574a(9) =262420a(10) =1048586a(11) =4195500a(12) =16777228a(13) =67112990a(14) =268436040a(15) =1073758360a(16) =4294967312a(17) =17179936830a(18) =68719476754a(19) =274878169880