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A086831
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Ramanujan sum c_n(2).
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4
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1, 1, -1, -2, -1, -1, -1, 0, 0, -1, -1, 2, -1, -1, 1, 0, -1, 0, -1, 2, 1, -1, -1, 0, 0, -1, 0, 2, -1, 1, -1, 0, 1, -1, 1, 0, -1, -1, 1, 0, -1, 1, -1, 2, 0, -1, -1, 0, 0, 0, 1, 2, -1, 0, 1, 0, 1, -1, -1, -2, -1, -1, 0, 0, 1, 1, -1, 2, 1, 1, -1, 0, -1, -1, 0, 2, 1, 1, -1, 0, 0, -1, -1, -2, 1, -1, 1, 0, -1, 0, 1, 2, 1, -1, 1, 0, -1, 0, 0, 0, -1, 1, -1, 0, -1
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OFFSET
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1,4
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COMMENTS
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Mobius transform of 1,2,0,0,0,0.. (A130779). - R. J. Mathar, Mar 24 2012
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976.
E. C. Titchmarsh, D. R. Heath-Brown, The theory of the Riemann zeta-function, 2nd edn., 1986
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LINKS
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Table of n, a(n) for n=1..105.
Wikipedia, Ramanujan's sum
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FORMULA
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For general k >= 1 c_n(k) = phi(n)*mu(n/gcd(n, k)) / phi(n/gcd(n, k)) so c_n(1) = mu(n) = A008683(n).
a(n) = phi(n)*mu(n/gcd(n, 2)) / phi(n/gcd(n, 2))
Dirichlet g.f. (1+2^(1-s))/zeta(s). [Titchmarsh eq. (1.5.4)] - R. J. Mathar, Mar 26 2011
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MAPLE
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with(numtheory):a:=n->phi(n)*mobius(n/gcd(n, 2))/phi(n/gcd(n, 2)): seq(a(n), n=1..130); (Deutsch)
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CROSSREFS
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Cf. A000010, A008683, A054532, A054533, A054534, A054535.
Sequence in context: A085975 A214088 A005091 * A191340 A211229 A111405
Adjacent sequences: A086828 A086829 A086830 * A086832 A086833 A086834
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KEYWORD
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sign,easy,mult
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 07 2003
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EXTENSIONS
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Corrected and extended by Emeric Deutsch, Dec 23 2004
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STATUS
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approved
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