%I #14 Aug 23 2023 08:41:20
%S 5,19,37,47,61,75
%N Numbers k such that S(24*(3*k-1)) <> 16*(3*k-1) mod 24*(3*k-1) where S(k) := Sum_{0<=a<n, 0<=b<n} (a+b*i)^n and i is the imaginary unit.
%t fu[n_] := fu[n] = Mod[Sum[PowerMod[i + j I, n, n], {i, 0, n - 1}, {j, 0, n - 1}], n]; Table[If[! fu[24(3n - 1)]/(3n - 1) == 16, Print[n]; n], {n, 1, 40}]
%Y Cf. A230308, A230309, A230310, A232056.
%K nonn,more,hard
%O 1,1
%A _José María Grau Ribas_, Nov 17 2013