cp's OEIS Frontend

A263014 a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n (mod n).

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