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 A035109 Numerators in expansion of a certain Dirichlet series. 1
 1, 1, 5, 1, 7, 5, 9, 1, 17, 7, 13, 5, 15, 9, 35, 1, 19, 17, 21, 7, 45, 13, 25, 5, 37, 15, 53, 9, 31, 35, 33, 1, 65, 19, 63, 17, 39, 21, 75, 7, 43, 45, 45, 13, 119, 25, 49, 5, 65, 37, 95, 15, 55, 53, 91, 9, 105, 31, 61, 35, 63, 33, 153, 1, 105, 65, 69, 19, 125, 63, 73, 17, 75, 39 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is also the number of orbits of length n for the map SxT where S has one orbit of each length and T has one orbit of each odd length. - Thomas Ward, Apr 08 2009 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 M. Baake and R. V. Moody, Similarity submodules and semigroups in Quasicrystals and Discrete Geometry, ed. J. Patera, Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp. 1-13. A. Pakapongpun, T. Ward, Functorial Orbit counting, JIS 12 (2009) 09.2.4, example 17. FORMULA Dirichlet g.f.: zeta(s)*Product((1+p^-s)/(1-p^(1-s))), p > 2. a(n) = (1/n)*sumdiv(n,d,mu(n/d)sum(d,e,e)sum(d,e odd only,e). - Thomas Ward, Apr 08 2009 EXAMPLE a(6) = (1/6)*(mu(6)*1*1 + mu(3)*3*1 + mu(2)*4*4 + mu(1)*4*12) = 5. - Thomas Ward, Apr 08 2009 MATHEMATICA a[n_] := (1/n)*DivisorSum[n, MoebiusMu[n/#]*DivisorSigma[1, #]*DivisorSum[ #, If[OddQ[#], #, 0]&]&]; Array[a, 80] (* Jean-François Alcover, Dec 07 2015, adapted from PARI *) PROG (PARI) a(n)=(1/n)*sumdiv(n, d, moebius(n/d)*sigma(d)*sumdiv(d, e, if(e%2, e, 0))) \\ Thomas Ward, Apr 08 2009 CROSSREFS Sequence in context: A198129 A244425 A332343 * A301509 A101263 A187561 Adjacent sequences: A035106 A035107 A035108 * A035110 A035111 A035112 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)