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For n >= 1, 1 = Sum_{n/2<=k<n, gcd(k,n)=1} a(k).
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%I #13 Oct 27 2019 05:09:52

%S 1,1,1,0,1,0,0,0,1,0,1,-1,-1,1,0,0,1,0,0,0,1,0,1,-2,-2,0,1,1,-1,1,0,1,

%T 1,0,3,-4,-3,1,1,1,6,-5,-5,0,0,6,3,-6,-2,-10,-2,13,0,-3,1,-12,-2,17,2,

%U -1,-2,-30,0,41,-1,-6,0,-22,3,22,2,-6,-3,-14,-2,15,-1,4,2,-27,8,24,2,-49,-7,-1,0,45,-2,-24,5,-89,0,83,5,25,-3,-9,-8,8

%N For n >= 1, 1 = Sum_{n/2<=k<n, gcd(k,n)=1} a(k).

%e The integers which are >= 9/2 and are < 9 and are coprime to 9 are 5,7,8. So a(5) + a(7) + a(8) = 1.

%t f[n_] := Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &]; g[l_] :=Append[l, 1 - Plus @@ l[[Most[f[Length[l] + 2]]]]];Nest[g, {}, 100] (* _Ray Chandler_, Nov 13 2006 *)

%Y Cf. A124406.

%K sign

%O 1,24

%A _Leroy Quet_, Oct 31 2006

%E Extended by _Ray Chandler_, Nov 13 2006