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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A101434 A293780 A048168 * A317705 A318692 A291441
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 16 2010
STATUS
approved

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Last modified July 23 13:44 EDT 2024. Contains 374549 sequences. (Running on oeis4.)