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!)
 A321322 a(n) = Sum_{d|n} mu(n/d)*J_2(d), where J_2() is the Jordan function (A007434). 1
 1, 2, 7, 9, 23, 14, 47, 36, 64, 46, 119, 63, 167, 94, 161, 144, 287, 128, 359, 207, 329, 238, 527, 252, 576, 334, 576, 423, 839, 322, 959, 576, 833, 574, 1081, 576, 1367, 718, 1169, 828, 1679, 658, 1847, 1071, 1472, 1054, 2207, 1008, 2304, 1152, 2009, 1503, 2807, 1152, 2737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Möbius transform applied twice to squares. LINKS N. J. A. Sloane, Transforms FORMULA G.f.: Sum_{k>=1} A007427(k)*x^k*(1 + x^k)/(1 - x^k)^3. a(n) = Sum_{d|n} mu(n/d)*phi(d)*psi(d), where phi() is the Euler totient function (A000010) and psi() is the Dedekind psi function (A001615). MATHEMATICA Table[Sum[MoebiusMu[n/d] Sum[MoebiusMu[d/j] j^2, {j, Divisors[d]}], {d, Divisors[n]}], {n, 55}] nmax = 55; Rest[CoefficientList[Series[Sum[DivisorSum[k, MoebiusMu[#] MoebiusMu[k/#] &] x^k (1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]] CROSSREFS Cf. A000010, A001615, A007427, A007431, A007433, A007434, A008683. Sequence in context: A293646 A020895 A174247 * A065139 A093916 A042451 Adjacent sequences:  A321319 A321320 A321321 * A321323 A321324 A321325 KEYWORD nonn,mult AUTHOR Ilya Gutkovskiy, Nov 04 2018 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 September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)