A038998 Sublattices of index n in generic 11-dimensional lattice.

1, 2047, 88573, 2794155, 12207031, 181308931, 329554457, 3269560515, 5883904390, 24987792457, 28531167061, 247486690815, 149346699503, 674597973479, 1081213356763, 3571013994483, 2141993519227, 12044352286330, 6471681049901, 34108336703805, 29189626919861

Offset

1,2

References

Michael Baake, "Solution of the coincidence problem in dimensions", 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=11.

Multiplicative with a(p^e) = Product_{k=1..10} (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^11, where c = Pi^30*zeta(3)*zeta(5)*zeta(7)*zeta(9)*zeta(11)/4962689060175000 = 0.208520... . - Amiram Eldar, Oct 19 2022

Mathematica

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 10}]; 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, A038999.

Sequence in context: A075954 A011561 A160960 * A068027 A075949 A075950

Adjacent sequences: A038995 A038996 A038997 * A038999 A039000 A039001

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