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%I #21 Jul 28 2017 22:00:30
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,16,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,32,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,24,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,64,0,0,0,0
%N a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n (mod n).
%C Sum of the n-th powers of the invertible elements of Z[i]/nZ[i].
%H Hans Havermann, <a href="/A263014/b263014.txt">Table of n, a(n) for n = 1..5000</a>
%t Sp[n_, k_] := Mod[Sum[If[GCD[a^2 + b^2, n] == 1, PowerMod[(a + b I), k, n], 0], {a, n}, {b, n}], n]; Table[ Sp[n, n] , {n, 1, 74}]
%Y See A263016 for indices where this is nonzero.
%Y See A290287 for the nonzero values.
%Y Cf. A231563, A231564, A231565.
%K nonn
%O 1,20
%A _José María Grau Ribas_, Oct 07 2015
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