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A339400 Mark each point on the n X n grid with the number of points that are visible from it; a(n) is the number of distinct values in the grid.

%I A339400 #52 Feb 05 2021 00:43:31
%S A339400 1,3,3,4,3,7,5,7,7,11,5,14,8,13,13,19,9,22,11,23,21,25,13,29,21,34,26,
%T A339400 37,11,40,26,44,31,45,21,54,35,54,36,55,24,65,40,59,47,70,24,71,43,72,
%U A339400 55,81,28,74,55,88,59,90,28,93,58,91,66,96,46,110,63,100
%N A339400 Mark each point on the n X n grid with the number of points that are visible from it; a(n) is the number of distinct values in the grid.
%C A339400 a(n) <= A008805(n). This is because A008805(n) is the maximum number of points required to calculate a(n) and each point is located in the first quadrant.
%H A339400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VisiblePoint.html">Visible Point</a>
%e A339400 a(1) = 1 because there are 3 visible points from every point on the grid.
%e A339400 a(2) = 3 because 5 points are visible from every vertex of the grid, 7 points are visible from the midpoint of every edge of the grid, and 8 points are visible from the middle of the grid.
%e A339400 a(3) = 3 because 9 points are visible from every vertex of the grid, 11 points are visible from the inner points of every edge of the grid, and 12 points are visible from every inner point of the grid.
%o A339400 (PARI) \\ n = side length, d = dimension
%o A339400 cdvps(n, d) ={my(m=Map());
%o A339400   forvec(u=vector(d, i, [0, n\2]),
%o A339400     my(c=0); forvec(v=[[t-n, t]|t<-u], c+=(gcd(v)==1));
%o A339400     mapput(m, c, 1), 1);
%o A339400   #m; }
%o A339400 a(n) = cdvps(n, 2)
%Y A339400 Cf. A008805, A049687, A049691, A300778, A331771.
%K A339400 nonn
%O A339400 1,2
%A A339400 _Torlach Rush_, Dec 02 2020