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 A263014 a(n) = Sum_{0 < a, b <= n and gcd(a^2 + b^2, n) = 1} (a + bi)^n  (mod n). 3
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,20 COMMENTS Sum of the n-th powers of the invertible elements of Z[i]/nZ[i]. LINKS Hans Havermann, Table of n, a(n) for n = 1..5000 MATHEMATICA 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}] CROSSREFS See A263016 for indices where this is nonzero. See A290287 for the nonzero values. Cf. A231563, A231564, A231565. Sequence in context: A199619 A036482 A273650 * A028721 A028664 A028717 Adjacent sequences:  A263011 A263012 A263013 * A263015 A263016 A263017 KEYWORD nonn AUTHOR José María Grau Ribas, Oct 07 2015 STATUS approved

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Last modified August 12 08:40 EDT 2022. Contains 356067 sequences. (Running on oeis4.)