%I A399232 #23 Sep 01 2026 11:39:12
%S A399232 6,20,42,54,110,156,210,272,342,420,506,500,486,812,930,1056,1190,
%T A399232 1332,1482,1640,1806,1890,2162,2058,2550,2756,2970,3192,3422,3660,
%U A399232 3780,4160,4422,4692,4970,5256,5250,5852,6162,4374,6806,7140,7482,7832,8190,8556,8930,9312,9504
%N A399232 a(n) = Sum_{k=1..4*n+2} (k^(4*n+1) mod (2*n+1)).
%C A399232 a(n) appears to satisfy rad(2*n+1) = (2*n+1)^2 / ((2*n+1)^2 - a(n)).
%C A399232 For m = 2*n+1, the equation a(n) = m*(m-1) appears to hold exactly when m belongs to A056911 (the odd squarefree numbers); when m belongs to A053850 (the odd nonsquarefree numbers), a(n) is not of the form x*(x-1) for any positive x.
%H A399232 James C. McMahon, <a href="/A399232/b399232.txt">Table of n, a(n) for n = 1..1000</a>
%t A399232 a[n_]:=Sum[Mod[k^(4n+1),2n+1],{k,1,4n+2}];Array[a,49] (* _James C. McMahon_, Aug 31 2026 *)
%Y A399232 Cf. A056911, A053850.
%K A399232 nonn
%O A399232 1,1
%A A399232 _Rui Ferreira_, Aug 23 2026