A035108 Denominators in expansion of a certain Dirichlet series.

1, 5, 11, 16, 25, 31, 41, 55, 61, 71, 80, 81, 101, 121, 125, 131, 151, 155, 176, 181, 191, 205, 211, 241, 251, 256, 271, 275, 281, 305, 311, 331, 341, 355, 361, 400, 401, 405, 421, 431, 451, 461, 491, 496, 505, 521, 541, 571, 601, 605, 625, 631, 641, 655, 656

Offset

1,2

Links

Table of n, a(n) for n=1..55.

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.

Ron Lifshitz, Theory of color symmetry for periodic and quasiperiodic crystals, Rev. Mod. Phys. 69, 1181 (1997). See row N = 10 of Table VII.

Formula

(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).

Prog

(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)}

Crossrefs

Sequence in context: A314180 A314181 A314182 * A022136 A042385 A041046

Adjacent sequences: A035105 A035106 A035107 * A035109 A035110 A035111

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved