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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.

These n are the numbers for which A141225(n) is odd. Note that n must be odd. When A141225(n)=1, the central point is the only point seeing the maximal number of points. Except for 1, these numbers are 3 or 11 (mod 12).

These numbers also seem to produce cubic n x n x n lattices in which the central point has maximal visibility; see A141228. Note that for n>3, n-1 is twice a prime in A141246.

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.

Sequence A141247 gives the minimum number of points visible from a point. By symmetry, when a(n) is odd, the central point in the lattice can see only the minimal number of points. When a(n)=1, the central point is the only such point. See A141249 for the n X n lattices that have such a central point.