The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A078439 a(n) = Sum_{k=1..n} gcd(k,n)*mu(gcd(k,n))^2. 2
 1, 3, 5, 4, 9, 15, 13, 8, 12, 27, 21, 20, 25, 39, 45, 16, 33, 36, 37, 36, 65, 63, 45, 40, 40, 75, 36, 52, 57, 135, 61, 32, 105, 99, 117, 48, 73, 111, 125, 72, 81, 195, 85, 84, 108, 135, 93, 80, 84, 120, 165, 100, 105, 108, 189, 104, 185, 171, 117, 180, 121, 183, 156, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{d|n} d*mu(d)^2*phi(n/d). Multiplicative with a(p) = 2*p-1 and a(p^e) = 2*(p-1)*p^(e-1), e>1. Dirichlet g.f.: zeta(s-1)^2 / (zeta(s) * zeta(2s-2)). - Álvar Ibeas, Mar 20 2015 Sum_{k=1..n} a(k) ~ 9 * n^2 * (2*log(n) + 4*gamma - 1 - 36*Zeta'(2)/Pi^2) / Pi^4, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 01 2019 MATHEMATICA Table[Sum[d*MoebiusMu[d]^2*EulerPhi[n/d], {d, Divisors[n]}], {n, 1, 100}] (* Vaclav Kotesovec, Feb 01 2019 *) PROG (PARI) vector(80, n, sumdiv(n, d, d*moebius(d)^2*eulerphi(n/d))) \\ Michel Marcus, Mar 20 2015 (MAGMA) [&+[Gcd(k, n)*MoebiusMu(Gcd(n, k))^2:k  in [1..n]]:n in [1..70]]; // Marius A. Burtea, Sep 15 2019 CROSSREFS Cf. A008683, A000010, A063659. Sequence in context: A255439 A177983 A294673 * A007063 A335500 A127397 Adjacent sequences:  A078436 A078437 A078438 * A078440 A078441 A078442 KEYWORD mult,nonn AUTHOR Vladeta Jovovic, Dec 31 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)