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A035108 Denominators in expansion of a certain Dirichlet series. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)