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Search: id:A100449
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| A100449 |
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Number of ordered pairs (i,j) with |i| + |j| <= n and GCD{i,j} <= 1. |
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+0
2
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| 1, 5, 9, 17, 25, 41, 49, 73, 89, 113, 129, 169, 185, 233, 257, 289, 321, 385, 409, 481, 513, 561, 601, 689, 721, 801, 849, 921, 969, 1081, 1113, 1233, 1297, 1377, 1441, 1537, 1585, 1729, 1801, 1897, 1961, 2121, 2169, 2337, 2417, 2513, 2601, 2785, 2849, 3017
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Note that GCD{0,k} = k for any k.
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FORMULA
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a(n) = 1+4*Sum(phi(k), k=1..n) = 1+4*A002088(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 25 2004
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MAPLE
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f:=proc(n) local i, j, k, t1, t2, t3; t1:=0; for i from -n to n do for j from -n to n do if abs(i) + abs(j) <= n then t2:=gcd(i, j); if t2 <= 1 then t1:=t1+1; fi; fi; od: od: t1; end;
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MATHEMATICA
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f[n_] := Length[ Union[ Flatten[ Table[ If[ Abs[i] + Abs[j] <= n && GCD[i, j] <= 1, {i, j}, {0, 0}], {i, -n, n}, {j, -n, n}], 1]]]; Table[ f[n], {n, 0, 49}] (from Robert G. Wilson v Dec 14 2004)
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CROSSREFS
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Cf. A018805, A100448, A100450, A027430, etc.
Adjacent sequences: A100446 A100447 A100448 this_sequence A100450 A100451 A100452
Sequence in context: A054278 A080335 A089109 this_sequence A081295 A059743 A000322
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KEYWORD
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nonn
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AUTHOR
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njas, Nov 21 2004
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EXTENSIONS
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I would also like to get the sequences of the numbers of distinct sums i+j (also distinct products i*j) over all ordered pairs (i,j) with |i| + |j| <= n; also over all ordered pairs (i,j) with |i| + |j| <= n and GCD{i,j} <= 1.
More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 25 2004
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