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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
OFFSET
1,20
COMMENTS
Sum of the n-th powers of the invertible elements of Z[i]/nZ[i].
LINKS
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.
Sequence in context: A199619 A036482 A273650 * A028721 A028664 A028717
KEYWORD
nonn
AUTHOR
STATUS
approved