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

1,2

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

Formula

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

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}]

Crossrefs

Sequence in context: A312979 A312980 A035104 * A064423 A312981 A312982

Adjacent sequences: A141221 A141222 A141223 * A141225 A141226 A141227

Keyword

nice,nonn

Author

T. D. Noe, Jun 15 2008

Status

approved