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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.
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%I #9 Oct 10 2019 13:54:42

%S 1,3,11,7,137,5,363,49,19,37,83711,7,1145993,167,19,1321,42142223,65,

%T 275295799,19,43,2887,444316699,133,127,1177,18469,85,9227046511387,

%U 23,290774257297357,3877999,212,22737,971,229,2040798836801833,233731,1039

%N 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.

%e 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.

%t 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 *)

%Y Cf. A126260, A126262.

%K frac,nonn

%O 1,2

%A _Leroy Quet_, Dec 22 2006

%E Extended by _Ray Chandler_, Dec 24 2006