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A175341
Number of coprime pairs (x,y) with x^2+y^2 <= n^2.
3
0, 4, 8, 16, 32, 48, 72, 88, 120, 152, 192, 224, 264, 312, 384, 440, 480, 544, 616, 672, 768, 832, 928, 1000, 1112, 1192, 1280, 1384, 1488, 1584, 1704, 1816, 1960, 2072, 2224, 2344, 2480, 2600, 2752, 2912, 3064, 3184, 3360, 3480, 3696, 3856, 4016, 4176
OFFSET
0,2
LINKS
J. Wu, On the primitive circle problem, Monatsh. Math. 135 (2002), 69.
W. G. Zhai and X.D. Cao, On the number of coprime integer pairs within a circle, Acta Arith. 90 (1999), 1.
FORMULA
a(n) = 4*A176562(n). - R. J. Mathar, May 07 2010
a(n) = A304651(n^2). - Seiichi Manyama, May 26 2018
EXAMPLE
a(2) = 8 counts (x,y) = (-1,-1), (-1,0), (-1,1), (0,-1), (0,1), (1,-1), (1,0) and (1,1).
MATHEMATICA
a89[n_] := a89[n] = Product[{p, e} = pe; Which[p < 3 && e == 1, 1, p == 2 && e > 1, 0, Mod[p, 4] == 1, 2, Mod[p, 4] == 3, 0, True, a89[p^e]], {pe, FactorInteger[n]}];
b[n_] := b[n] = If[n == 0, 0, b[n-1] + 4 a89[n]];
a[n_] := b[n^2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 02 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 16 2010
STATUS
approved