A290287 -id:A290287 - 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).

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

José María Grau Ribas, Oct 07 2015

nonn

Sum of the n-th powers of the invertible elements of Z[i]/nZ[i].

Hans Havermann, Table of n, a(n) for n = 1..5000

See A263016 for indices where this is nonzero.
See A290287 for the nonzero values.
Cf. A231563, A231564, A231565.

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}]

A263016 Numbers n such that A263014(n) > 0.

Original entry on oeis.org

20, 24, 40, 48, 60, 80, 96, 120, 140, 156, 160, 180, 192, 240, 260, 272, 280, 312, 320, 336, 340, 360, 384, 408, 420, 460, 468, 480, 520, 540, 544, 560, 580, 600, 624, 640, 672, 680, 696, 720, 740, 768, 780

Offset: 1

José María Grau Ribas, Oct 07 2015

nonn

Hans Havermann, Table of n, a(n) for n = 1..530

Cf. A263014, A263015, A290287.

sumin[n_, k_] := Mod[Sum[If[GCD[i, n] == 1, PowerMod[i, k, n], 0], {i, 1, n}], n]; Select[Range[100], sumin[#, #] > 0 &]

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).

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