A038999 - OEIS

%I #24 Oct 21 2022 10:12:23

%S 1,4095,265720,11180715,61035156,1088123400,2306881200,26167664835,

%T 52955405230,249938963820,313842837672,2970939589800,1941507093540,

%U 9446678514000,16218261652320,57162391576563,36413889826860,216852384416850,122961939948120,682416684216540

%N Sublattices of index n in generic 12-dimensional lattice.

%D 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.

%H Amiram Eldar, <a href="/A038999/b038999.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=12.

%F Multiplicative with a(p^e) = Product_{k=1..11} (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^12, where c = Pi^42*zeta(3)*zeta(5)*zeta(7)*zeta(9)*zeta(11)/3456808210410967912500000 = 0.191191... . - _Amiram Eldar_, Oct 19 2022

%t 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 *)

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

%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