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A063985
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Partial sums of cototient sequence A051953.
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7
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0, 1, 2, 4, 5, 9, 10, 14, 17, 23, 24, 32, 33, 41, 48, 56, 57, 69, 70, 82, 91, 103, 104, 120, 125, 139, 148, 164, 165, 187, 188, 204, 217, 235, 246, 270, 271, 291, 306, 330, 331, 361, 362, 386, 407, 431, 432, 464, 471, 501, 520, 548, 549, 585, 600, 632, 653, 683
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OFFSET
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1,3
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COMMENTS
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Number of elements in the set {(x,y): 1<=x<=y<=n, 1=gcd(x,y)}; a(n) = A000217(n) - A002088(n) = A100613(n) - A185670(n). - Reinhard Zumkeller, Jan 21 2013
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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a(n) = Sum_{x=1..n} x-phi(x), = Sum(x)-Sum(phi(x)) = A000217(n)-A002088(n), phi(n) = A000010(n), cototient(n) = A051953(n).
a(n) = n^2 - A091369(n). - Enrique Pérez Herrero, Feb 25 2012
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MATHEMATICA
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f[n_] := n(n + 1)/2 - Sum[ EulerPhi@i, {i, n}]; Array[f, 58] (* Robert G. Wilson v *)
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PROG
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(PARI) { a=0; for (n=1, 1000, write("b063985.txt", n, " ", a+=n - eulerphi(n)) ) } [From Harry J. Smith, Sep 04 2009]
(Haskell)
a063985 n = length [()| x <- [1..n], y <- [x..n], gcd x y > 1]
-- Reinhard Zumkeller, Jan 21 2013
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CROSSREFS
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Cf. A000010, A051953, A002088, A048290, A000217.
Sequence in context: A113755 A167180 A091271 * A050052 A071349 A039891
Adjacent sequences: A063982 A063983 A063984 * A063986 A063987 A063988
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Sep 06 2001
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EXTENSIONS
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Corrected by Robert G. Wilson v, Dec 13 2006
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STATUS
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approved
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