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

Terms

a(0) =2a(1) =3a(2) =7a(3) =8a(4) =22a(5) =24a(6) =25a(7) =28a(8) =29a(9) =36a(10) =37a(11) =38a(12) =40a(13) =41a(14) =45a(15) =46a(16) =70a(17) =72a(18) =73a(19) =76a(20) =77a(21) =85a(22) =86a(23) =87a(24) =89a(25) =90a(26) =95a(27) =96a(28) =178a(29) =180