A024828 a(n) = least m such that if r and s in {h/(1 + h^2): h = 1,2,...,n} satisfy r > s, then r > k/m > s for some integer k.

7, 9, 11, 14, 18, 27, 32, 44, 58, 66, 83, 102, 112, 134, 158, 184, 198, 227, 258, 291, 308, 344, 382, 422, 464, 486, 531, 578, 627, 678, 704, 758, 814, 872, 932, 994, 1026, 1091, 1158, 1227, 1298, 1371, 1408, 1484, 1562, 1642, 1724, 1808, 1894, 1938, 2027, 2118, 2211, 2306