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A038993
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Sublattices of index n in generic 6-dimensional lattice.
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12
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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
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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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.
Index entries for sequences related to sublattices.
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Offset changed from 0 to 1 by R. J. Mathar, Mar 31 2011
More terms from Amiram Eldar, Aug 29 2019
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STATUS
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approved
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