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A059743 Number of points of norm^2 <= n^2 in the square lattice that are visible from the origin. 1
1, 5, 9, 17, 33, 49, 73, 89, 121, 153, 193, 225, 265, 313, 385, 441, 481, 545, 617, 673, 769, 833, 929, 1001, 1113, 1193, 1281, 1385, 1489, 1585, 1705, 1817, 1961, 2073, 2225, 2345, 2481, 2601, 2753, 2913, 3065, 3185, 3361, 3481, 3697, 3857, 4017, 4177 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A lattice point (i,j) is "visible" from the origin if no other lattice point lies on the line segment from (0,0) to (i,j), which is equivalent to saying that i and j are relatively prime. By convention, we say that (0,0) is visible from the origin.
REFERENCES
Tom M. Apostol, "Introduction to Analytic Number Theory", Springer-Verlag, Section 3.8.
LINKS
MAPLE
N:= 100; # to get a(0) to a(N)
for n from 1 to N do
C[n]:= Array(1..n, j -> `if`(igcd(n, j)=1, 1, 0)):
B[n]:= map(round, Statistics[CumulativeSum](C[n]));
od:
1, 5, 9, seq(1 + 8*(add(numtheory[phi](x), x=1..floor(n/sqrt(2)))+add(B[x][floor(sqrt(n^2-x^2))], x=ceil(n/sqrt(2))..n-1)), n = 3 .. N); # Robert Israel, Jun 15 2014
CROSSREFS
See also A000328, where visibility is not required.
Sequence in context: A160426 A301786 A258411 * A000322 A205539 A020737
KEYWORD
nonn
AUTHOR
John W. Layman, Oct 13 2001
STATUS
approved

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)