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A085097 Ramanujan sum c_n(3). 7
1, -1, 2, 0, -1, -2, -1, 0, -3, 1, -1, 0, -1, 1, -2, 0, -1, 3, -1, 0, -2, 1, -1, 0, 0, 1, 0, 0, -1, 2, -1, 0, -2, 1, 1, 0, -1, 1, -2, 0, -1, 2, -1, 0, 3, 1, -1, 0, 0, 0, -2, 0, -1, 0, 1, 0, -2, 1, -1, 0, -1, 1, 3, 0, 1, 2, -1, 0, -2, -1, -1, 0, -1, 1, 0, 0, 1, 2, -1, 0, 0, 1, -1, 0, 1, 1, -2, 0, -1, -3, 1, 0, -2, 1, 1, 0, -1, 0, 3, 0, -1, 2, -1, 0, 2, 1, -1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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 ed, (1986)

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Wikipedia, Ramanujan's sum

FORMULA

a(n) = phi(n)*mu(n/gcd(n, 3)) / phi(n/gcd(n, 3)).

Dirichlet g.f.: (1+3^(1-s))/zeta(s). [Titchmarsh eq. (1.5.4.)] - R. J. Mathar, Mar 26 2011

MATHEMATICA

f[list_, i_] := list[[i]]; nn = 105; a =Table[MoebiusMu[n], {n, 1, nn}]; b =Table[If[IntegerQ[3/n], n, 0], {n, 1, nn}]; Table[DirichletConvolve[f[a, n], f[b, n], n, m], {m, 1, nn}] (* Geoffrey Critzer, Dec 30 2015 *)

PROG

(PARI) a(n)=eulerphi(n)*moebius(n/gcd(n, 3))/eulerphi(n/gcd(n, 3))

CROSSREFS

Cf. A086831, A085906.

Sequence in context: A092928 A321090 A219026 * A117997 A079684 A033761

Adjacent sequences:  A085094 A085095 A085096 * A085098 A085099 A085100

KEYWORD

sign,easy,mult

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 10 2003

EXTENSIONS

More terms from Benoit Cloitre, Aug 12 2003

STATUS

approved

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Last modified April 21 20:41 EDT 2019. Contains 322328 sequences. (Running on oeis4.)