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

1,2

Links

Table of n, a(n) for n=1..39.

Example

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.

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 *)

Crossrefs

Cf. A126260, A126262.

Sequence in context: A250034 A006495 A112286 * A050097 A330566 A361974

Adjacent sequences: A126258 A126259 A126260 * A126262 A126263 A126264

Keyword

frac,nonn

Author

Leroy Quet, Dec 22 2006

Extensions

Extended by Ray Chandler, Dec 24 2006

Status

approved