|
| |
|
|
A086831
|
|
Ramanujan sum c_n(2).
|
|
3
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
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: A134022 A085975 A005091 * A191340 A111405 A089053
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 (deutsch(AT)duke.poly.edu), Dec 23 2004
|
| |
|
|
