A038997 - OEIS

%I #26 May 08 2023 21:49:59

%S 1,1023,29524,698027,2441406,30203052,47079208,408345795,653757313,

%T 2497558338,2593742460,20608549148,11488207654,48162029784,

%U 72080070744,222984027123,125999618778,668793731199,340614792100,1704167305962,1389966536992,2653398536580,1883023236984

%N Number of sublattices of index n in generic 10-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="/A038997/b038997.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=10.

%F Multiplicative with a(p^e) = Product_{k=1..9} (p^(e+k)-1)/(p^k-1).

%F Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k). - _R. J. Mathar_, Apr 01 2011

%F Sum_{k=1..n} a(k) ~ c * n^10, where c = Pi^30*zeta(3)*zeta(5)*zeta(7)*zeta(9) / 4511535509250000 = 0.229259... . - _Amiram Eldar_, Oct 19 2022

%t f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 9}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)

%Y Column 10 of A160870.

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