

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
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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

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. 113.


FORMULA

Dirichlet g.f.: zeta(s)*Product((1+p^s)/(1p^(1s))), 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] (* JeanFrançois 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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



