A230761 -id:A230761 - cp's OEIS frontend

A230308 Numbers k such that the sum over the k-th powers of all Gaussian integers in the k X k base square in the first quadrant is == 0 (mod k).

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 1

José María Grau Ribas, Oct 15 2013

nonn

Define S(k) = Sum_{0<=a=1. Then this sequence contains all places k such that S(k) == 0 (mod k).

The asymptotic density of this sequence is 0.971000... (Fortuny Ayuso et al., 2014). - Amiram Eldar, May 01 2021

Amiram Eldar, Table of n, a(n) for n = 1..10000
Pedro Fortuny Ayuso, Jose Maria Grau and Antonio Oller-Marcen, A von Staudt-type formula for Sum_{z in Zn[i]} z^k, arXiv:1402.0333 [math.NT], 2014.

The complement of A230761.

Cf. A230309, A230310, A073763.

aa[n_] := aa[n] = Mod[Sum[PowerMod[a + b I, n, n], {a,n}, {b, n}], n];Select[Range[100], aa[#] == 0 &]

cp's OEIS Frontend

A230308 Numbers k such that the sum over the k-th powers of all Gaussian integers in the k X k base square in the first quadrant is == 0 (mod k).

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