A038994 Number of sublattices of index n in generic 7-dimensional lattice.

1, 127, 1093, 10795, 19531, 138811, 137257, 788035, 896260, 2480437, 1948717, 11798935, 5229043, 17431639, 21347383, 53743987, 25646167, 113825020, 49659541, 210837145, 150021901, 247487059, 154764793, 861322255, 317886556, 664088461, 678468820, 1481689315

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=7.

Multiplicative with a(p^e) = Product_{k=1..6} (p^(e+k)-1)/(p^k-1).

Sum_{k=1..n} a(k) ~ c * n^7, where c = Pi^12*zeta(3)*zeta(5)*zeta(7)/3572100 = 0.325206... . - Amiram Eldar, Oct 19 2022

Mathematica

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 6}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Crossrefs

Column 7 of A160870.

Cf. A001001, A038991, A038992, A038993, A038995, A038996, A038997, A038998, A038999.

Sequence in context: A077361 A225148 A160897 * A068023 A194257 A243529

Adjacent sequences: A038991 A038992 A038993 * A038995 A038996 A038997

Keyword

nonn,mult

Author

N. J. A. Sloane

Extensions

More terms from Amiram Eldar, Aug 29 2019

Status

approved