A038995 Number of sublattices of index n in generic 8-dimensional lattice.

1, 255, 3280, 43435, 97656, 836400, 960800, 6347715, 8069620, 24902280, 21435888, 142466800, 67977560, 245004000, 320311680, 866251507, 435984840, 2057753100, 943531280, 4241688360, 3151424000, 5466151440, 3559590240, 20820505200, 7947261556, 17334277800, 18326727760

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

Index entries for sequences related to sublattices

Formula

f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=8.

Multiplicative with a(p^e) = Product_{k=1..7} (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^8, where c = Pi^20*zeta(3)*zeta(5)*zeta(7)/43401015000 = 0.285716... . - Amiram Eldar, Oct 19 2022

Mathematica

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 7}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Crossrefs

Column 8 of A160870.

Cf. A001001, A038991, A038992, A038993, A038994, A038996, A038997, A038998, A038999.

Sequence in context: A204738 A206048 A160908 * A068024 A028524 A075940

Adjacent sequences: A038992 A038993 A038994 * A038996 A038997 A038998

Keyword

nonn,mult

Author

N. J. A. Sloane

Extensions

Offset set to 1 by R. J. Mathar, Mar 01 2011

More terms from Amiram Eldar, Aug 29 2019

Status

approved