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A035109
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Numerators in expansion of a certain Dirichlet series.
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0
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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; internal format)
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OFFSET
| 0,3
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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. [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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REFERENCES
| Apisit Pakapongpun and Thomas Ward, Functorial orbit counting, Journal of Integer Sequences, 12 (2009) Article 09.2.4. [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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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. 1-13.
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FORMULA
| 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) [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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EXAMPLE
| a(6)=(1/6)(mu(6)*1*1+mu(3)*3*1+mu(2)*4*4+mu(1)*4*12)=5 [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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PROG
| (PARI) a(n)=(1/n)*sumdiv(n, d, moebius(n/d)*sigma(d)*sumdiv(d, e, if(e%2, e, 0))) [From Thomas Ward (t.ward(AT)uea.ac.uk), Apr 08 2009]
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CROSSREFS
| Sequence in context: A021663 A099218 A198129 * A101263 A187561 A088515
Adjacent sequences: A035106 A035107 A035108 * A035110 A035111 A035112
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), May 25 2010
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