A141227 Maximum number of points visible from some point in a cubic n x n x n lattice.

1, 8, 27, 57, 111, 183, 303, 435, 633, 843, 1155, 1443, 1893, 2313, 2895, 3447, 4215, 4875, 5865, 6723, 7887, 8943, 10371, 11553, 13293, 14745, 16707, 18411, 20703, 22485, 25257, 27459, 30423, 32931, 36291, 38889, 42837, 45950, 50115, 53523

Offset

1,2

Comments

Two points (a,b,c) and (d,e,f) are visible to each other when gcd(d-a,e-b,f-c)=1. Sequence A141228 gives the number of lattice points that have maximal visibility.

Links

Table of n, a(n) for n=1..40.

Eric Weisstein, MathWorld: Visible Point

Formula

The maximum number of visible points is slightly more than c*n^3, with c = 1/zeta(3) = 0.831907... (A088453).

Mathematica

Table[mx=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], {d, n}, {e, n}, {f, n}]; mx, {n, 10}]

Crossrefs

Cf. A141224.

Sequence in context: A223950 A339897 A131620 * A224134 A213488 A151675

Adjacent sequences: A141224 A141225 A141226 * A141228 A141229 A141230

Keyword

nonn

Author

T. D. Noe, Jun 15 2008

Status

approved