A263016 -id:A263016 - 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}]

A290287 Nonzero entries in A263014 in order of appearance.

Original entry on oeis.org

8, 16, 32, 16, 24, 48, 64, 16, 84, 12, 32, 36, 64, 64, 52, 128, 56, 48, 128, 96, 68, 144, 256, 136, 252, 184, 108, 256, 208, 324, 512, 224, 232, 400, 192, 512, 384, 272, 232, 576, 148, 256, 36, 616, 208, 168, 344, 736, 432, 564, 64, 196, 328, 864, 204, 832, 212, 216, 960, 420, 896, 928, 400, 768, 1008, 424, 768, 480, 576

Offset: 1