A141228 - OEIS

%I #2 Mar 30 2012 17:22:50

%S 1,8,1,8,20,64,20,32,64,216,13,432,64,64,20,32,8,32,32,216,64,64,27,8,

%T 64,216,7,32,64,352,32,216,8,8,125,64,8,24,1,8,64,8,32,24,8,8,27,8,8,8

%N Number of points having maximal visibility in a cubic n x n x n lattice.

%C Sequence A141227 gives the maximum number of points visible from some point. By symmetry, when a(n) is odd, the central point in the lattice can see the maximal number of points. When a(n)=1, the central point is the only such point. Apparently the numbers n in A141226 produce both the n x n and n x n x n lattices having central points with maximum visibility.

%t Table[mx=0; pts=0; Do[cnt=0; Do[If[GCD[d-a,e-b,f-c]<2, cnt++ ], {a,n}, {b,n}, {c,n}]; If[cnt>mx, mx=cnt; pts=1, If[cnt==mx, pts++ ]], {d,n}, {e,n}, {f,n}]; pts, {n,10}]

%Y Cf. A141225.

%K nonn

%O 1,2

%A _T. D. Noe_, Jun 15 2008