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 A086831 Ramanujan sum c_n(2). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Mobius transform of 1,2,0,0,0,0.. (A130779). - R. J. Mathar, Mar 24 2012 REFERENCES 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 LINKS Wikipedia, Ramanujan's sum FORMULA 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 MAPLE with(numtheory):a:=n->phi(n)*mobius(n/gcd(n, 2))/phi(n/gcd(n, 2)): seq(a(n), n=1..130); (Deutsch) CROSSREFS Cf. A000010, A008683, A054532, A054533, A054534, A054535. Sequence in context: A085975 A214088 A005091 * A191340 A211229 A111405 Adjacent sequences:  A086828 A086829 A086830 * A086832 A086833 A086834 KEYWORD sign,easy,mult AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 07 2003 EXTENSIONS Corrected and extended by Emeric Deutsch, Dec 23 2004 STATUS approved

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