f[n_] := Block[{k = 1}, While[ GCD[n(n + 1)/2, (n + k)(n + k + 1)/2] != 1, k++ ]; k]; t = Table[0, {1000}]; Do[a = f@n; If[a < 1001 && t[[a]] == 0, t[[a]] = n; Print[{a, n}], If[a > 1000, Print[{"Over 1000", n}]]], {n, 2^31 - 1}] (*
Robert G. Wilson v, Jun 03 2007 *)
