A141224 Maximum number of points visible from some point in a square n X n lattice.

1, 4, 9, 13, 19, 25, 35, 43, 55, 65, 81, 91, 111, 125, 147, 163, 187, 203, 233, 251, 283, 305, 337, 359, 399, 422, 465, 491, 531, 553, 609, 636, 691, 721, 769, 799, 863, 896, 961, 993, 1051, 1085, 1159, 1199, 1267, 1313, 1377, 1416, 1501, 1547, 1627, 1679

Offset: 1

Author

T. D. Noe, Jun 15 2008

Keywords

• nice
• nonn

Comments

Two points (a,b) and (c,d) are visible to each other when gcd(c-a,d-b)=1. Sequence A141225 gives the number of lattice points that have maximal visibility.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein, MathWorld: Visible Point

Programs

Mathematica

Table[mx=0; Do[cnt=0; Do[If[GCD[c-a,d-b]<2, cnt++ ], {a,n}, {b,n}]; If[cnt>mx, mx=cnt], {c,n}, {d,n}]; mx, {n,20}]

Formula

The maximum number of visible points is slightly more than c*n^2, with c = 6/Pi^2.