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%I #23 Oct 21 2022 10:11:38
%S 1,2047,88573,2794155,12207031,181308931,329554457,3269560515,
%T 5883904390,24987792457,28531167061,247486690815,149346699503,
%U 674597973479,1081213356763,3571013994483,2141993519227,12044352286330,6471681049901,34108336703805,29189626919861
%N Sublattices of index n in generic 11-dimensional lattice.
%D 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.
%H Amiram Eldar, <a href="/A038998/b038998.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>.
%F f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=11.
%F Multiplicative with a(p^e) = Product_{k=1..10} (p^(e+k)-1)/(p^k-1).
%F Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k).
%F 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
%t 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 *)
%Y Cf. A001001, A038991, A038992, A038993, A038994, A038995, A038996, A038997, A038999.
%K nonn,mult
%O 1,2
%A _N. J. A. Sloane_
%E Offset set to 1 by _R. J. Mathar_, Apr 01 2011
%E More terms from _Amiram Eldar_, Aug 29 2019
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