A038999 Sublattices of index n in generic 12-dimensional lattice.

1, 4095, 265720, 11180715, 61035156, 1088123400, 2306881200, 26167664835, 52955405230, 249938963820, 313842837672, 2970939589800, 1941507093540, 9446678514000, 16218261652320, 57162391576563, 36413889826860, 216852384416850, 122961939948120, 682416684216540

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=12.

Multiplicative with a(p^e) = Product_{k=1..11} (p^(e+k)-1)/(p^k-1).

Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k).

Sum_{k=1..n} a(k) ~ c * n^12, where c = Pi^42*zeta(3)*zeta(5)*zeta(7)*zeta(9)*zeta(11)/3456808210410967912500000 = 0.191191... . - Amiram Eldar, Oct 19 2022

Mathematica

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 11}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Crossrefs

Cf. A001001, A038991, A038992, A038993, A038994, A038995, A038996, A038997, A038998.

Sequence in context: A326705 A326383 A160972 * A022528 A024010 A123868

Adjacent sequences: A038996 A038997 A038998 * A039000 A039001 A039002

Keyword

nonn,mult

Author

N. J. A. Sloane

Extensions

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

More terms from Amiram Eldar, Aug 29 2019

Status

approved