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 A035108 Denominators in expansion of a certain Dirichlet series. 0

%I #11 Oct 04 2019 10:47:51

%S 1,5,11,16,25,31,41,55,61,71,80,81,101,121,125,131,151,155,176,181,

%T 191,205,211,241,251,256,271,275,281,305,311,331,341,355,361,400,401,

%U 405,421,431,451,461,491,496,505,521,541,571,601,605,625,631,641,655,656

%N Denominators in expansion of a certain Dirichlet series.

%H M. Baake and R. V. Moody, <a href="http://www.math.uni-bielefeld.de/baake/ps/fields3.ps.gz">Similarity submodules and semigroups</a> in Quasicrystals and Discrete Geometry, ed. J. Patera, Fields Institute Monographs, vol. 10 AMS, Providence, RI (1998) pp. 1-13.

%H Ron Lifshitz, <a href="https://doi.org/10.1103/RevModPhys.69.1181">Theory of color symmetry for periodic and quasiperiodic crystals</a>, Rev. Mod. Phys. 69, 1181 (1997). See row N = 10 of Table VII.

%F (1-5^(-s))^(-1) * Product_{p == 1 mod 5} (1-p^(-s))^(-4) * Product_{p == 4 mod 5} (1-p^(-2s))^(-2) * Product_{p == +- 2 mod 5} (1-p^(-4s))^(-1).

%o (PARI) {an=vector(64); v=direuler(p=2,800,1/[1-X,(1-X)^4,1-X^4,1-X^4,(1-X^2)^2][p%5+1]); c=0; for(n=1,length(v),if(v[n],c++; an[c]=n)); print(an)}

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified October 3 10:22 EDT 2023. Contains 365859 sequences. (Running on oeis4.)