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

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

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