a(n) = Sum_{k=1..n} floor( 1/{k/sqrt(2)} ), where {x} := x - floor(x).

Terms

a(0) =1a(1) =3a(2) =11a(3) =12a(4) =13a(5) =17a(6) =18a(7) =19a(8) =21a(9) =35a(10) =36a(11) =38a(12) =43a(13) =44a(14) =45a(15) =48a(16) =96a(17) =97a(18) =99a(19) =106a(20) =107a(21) =108a(22) =111a(23) =112a(24) =113a(25) =115a(26) =125a(27) =126a(28) =127a(29) =131