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 A038993 Sublattices of index n in generic 6-dimensional lattice. 12
 1, 63, 364, 2667, 3906, 22932, 19608, 97155, 99463, 246078, 177156, 970788, 402234, 1235304, 1421784, 3309747, 1508598, 6266169, 2613660, 10417302, 7137312, 11160828, 6728904, 35364420, 12714681, 25340742, 25095280, 52294536, 21243690, 89572392, 29583456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Michael Baake, "Solution of the coincidence problem in dimensions d <= 4", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 M. Baake and N. Neumarker, A Note on the Relation Between Fixed Point and Orbit Count Sequences, JIS 12 (2009) 09.4.4, Section 3. FORMULA f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=6. Multiplicative with a(p^e) = product (p^(e+k)-1)/(p^k-1), k=1..5. Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)*zeta(s-3)*zeta(s-4)*zeta(s-5). Dirichlet convolution of A038992 with A000584. - R. J. Mathar, Mar 31 2011 Sum_{k=1..n} a(k) ~ c * n^6, where c = Pi^12*zeta(3)*zeta(5)/3061800 = 0.376266... . - Amiram Eldar, Oct 19 2022 MATHEMATICA f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 5}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *) CROSSREFS Cf. A001001, A038991, A038992, A038994, A038995, A038996, A038997, A038998, A038999. Sequence in context: A034817 A160895 A203556 * A068022 A131993 A251019 Adjacent sequences: A038990 A038991 A038992 * A038994 A038995 A038996 KEYWORD nonn,mult AUTHOR EXTENSIONS Offset changed from 0 to 1 by R. J. Mathar, Mar 31 2011 More terms from Amiram Eldar, Aug 29 2019 STATUS approved

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)