A126261 a(n) is the numerator of the sum of the reciprocals of the positive integers k, k<=n, where every positive integer <= k and coprime to k is also coprime to n.
1, 3, 11, 7, 137, 5, 363, 49, 19, 37, 83711, 7, 1145993, 167, 19, 1321, 42142223, 65, 275295799, 19, 43, 2887, 444316699, 133, 127, 1177, 18469, 85, 9227046511387, 23, 290774257297357, 3877999, 212, 22737, 971, 229, 2040798836801833, 233731, 1039
Offset: 1
Examples
The positive integers k, k <= 6, where every positive integer <=k and coprime to k is also coprime to 6, are 1,2,6. So a(6) = 5 is the numerator of 1 +1/2 +1/6 = 5/3.
Programs
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Mathematica
f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Plus @@ (1/# &) /@ Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &];Table[Numerator[g[n]], {n, 40}] (* Ray Chandler, Dec 24 2006 *)
Extensions
Extended by Ray Chandler, Dec 24 2006