cp's OEIS Frontend

A230761 Indices k where the sum over k-th powers of the integers in a k X k square in the Gaussian plane (A230308) is not == 0 (mod k).

%I A230761 #14 May 01 2021 06:54:23
%S A230761 24,48,96,120,168,192,240,264,312,336,384,408,456,480,528,552,600,624,
%T A230761 672,696,744,768,816,840,888,912,960,984,1008,1032,1056,1104,1128,
%U A230761 1176,1200,1248,1272,1320,1344,1392,1416,1464
%N A230761 Indices k where the sum over k-th powers of the integers in a k X k square in the Gaussian plane (A230308) is not == 0 (mod k).
%C A230761 Define S(k) = Sum_{0<=a<k; 0<=b<k} (a+i*b)^k, where i is the imaginary unit. The sequence contains the places k where S(k) <> 0 (mod k).
%C A230761 Almost the same as A073763, but contains also 1008 (equivalent to A230310(1)), for example.
%C A230761 The asymptotic density of this sequence is 0.028999... (Fortuny Ayuso et al., 2014). - _Amiram Eldar_, May 01 2021
%H A230761 Amiram Eldar, <a href="/A230761/b230761.txt">Table of n, a(n) for n = 1..300</a>
%H A230761 Pedro Fortuny Ayuso, Jose Maria Grau and Antonio Oller-Marcen, <a href="http://arxiv.org/abs/1402.0333">A von Staudt-type formula for Sum_{z in Zn[i]} z^k</a>,  arXiv:1402.0333 [math.NT], 2014.
%Y A230761 The complement of A230308.
%Y A230761 Cf. A073763, A230309, A230310.
%K A230761 nonn
%O A230761 1,1
%A A230761 _Jose Maria Grau Ribas_, Oct 16 2013