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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 Seiichi Manyama, Table of n, a(n) for n = 0..10000 Wikipedia, Gauss circle problem 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 Cf. A000328, A176562, A304651. Sequence in context: A101434 A293780 A048168 * A317705 A318692 A291441 Adjacent sequences: A175338 A175339 A175340 * A175342 A175343 A175344 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.)