a(n) = Sum_{k=1..n} floor(1/{k*sqrt(6)}) where {x} := x - floor(x).

Terms

a(0) =2a(1) =3a(2) =5a(3) =6a(4) =10a(5) =11a(6) =17a(7) =18a(8) =40a(9) =42a(10) =43a(11) =45a(12) =46a(13) =49a(14) =50a(15) =55a(16) =56a(17) =67a(18) =68a(19) =69a(20) =71a(21) =72a(22) =74a(23) =75a(24) =79a(25) =80a(26) =87a(27) =88a(28) =116a(29) =118