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A038997
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Number of sublattices of index n in generic 10-dimensional lattice.
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12
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1, 1023, 29524, 698027, 2441406, 30203052, 47079208, 408345795, 653757313, 2497558338, 2593742460, 20608549148, 11488207654, 48162029784, 72080070744, 222984027123, 125999618778, 668793731199, 340614792100, 1704167305962, 1389966536992, 2653398536580, 1883023236984
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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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FORMULA
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f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=10.
Multiplicative with a(p^e) = Product_{k=1..9} (p^(e+k)-1)/(p^k-1).
Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k). - R. J. Mathar, Apr 01 2011
Sum_{k=1..n} a(k) ~ c * n^10, where c = Pi^30*zeta(3)*zeta(5)*zeta(7)*zeta(9) / 4511535509250000 = 0.229259... . - 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, 9}]; 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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KEYWORD
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nonn,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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