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gcd(1,2n)*1^2n + ...+ gcd(i,2n)*i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).
1

%I #11 Feb 05 2014 11:20:34

%S 1,2,3,4,5,10,7,8,9,2,11,4,13,14,15,16,17,30,19,20,27,22,23,24,25,26,

%T 27,28,29,30,31,32,33,34,35,12,37,38,39,72,41,58,43,44,45,46,47,80,49,

%U 10,51,52,53,90,105,56,57,58,59,60,61,62,63,64,65,66,67

%N gcd(1,2n)*1^2n + ...+ gcd(i,2n)*i^2n + ... + gcd(2n,2n)*2n^2n (mod 2n).

%t Su[n_] := Su[n] = Mod[Sum[GCD[i, n]*PowerMod[i, n, n], {i, 1, n}], n];Table[Su[2n],{n,1,44}]

%Y Gf. A231563, A231567.

%K nonn

%O 1,2

%A _José María Grau Ribas_, Dec 09 2013