cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A038996 Number of sublattices of index n in generic 9-dimensional lattice.

This page as a plain text file.
%I A038996 #28 May 08 2023 21:50:02
%S A038996 1,511,9841,174251,488281,5028751,6725601,50955971,72636421,249511591,
%T A038996 235794769,1714804091,883708281,3436782111,4805173321,13910980083,
%U A038996 7411742281,37117211131,17927094321,85083452531,66186639441,120491126959,81870575521,501457710611,198682027181
%N A038996 Number of sublattices of index n in generic 9-dimensional lattice.
%D A038996 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 A038996 Amiram Eldar, <a href="/A038996/b038996.txt">Table of n, a(n) for n = 1..10000</a>
%H A038996 <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>.
%F A038996 f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=9.
%F A038996 Multiplicative with a(p^e) = Product_{k=1..8} (p^(e+k)-1)/(p^k-1).
%F A038996 Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k). - _R. J. Mathar_, Apr 01 2011
%F A038996 Sum_{k=1..n} a(k) ~ c * n^9, where c = Pi^20*zeta(3)*zeta(5)*zeta(7)*zeta(9) / 38578680000 = 0.254479... . - _Amiram Eldar_, Oct 19 2022
%t A038996 f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 8}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)
%Y A038996 Column 9 of A160870.
%Y A038996 Cf. A001001, A038991, A038992, A038993, A038994, A038995, A038997, A038998, A038999.
%K A038996 nonn,mult
%O A038996 1,2
%A A038996 _N. J. A. Sloane_
%E A038996 Offset changed to 1 by _R. J. Mathar_, Apr 01 2011
%E A038996 More terms from _Amiram Eldar_, Aug 29 2019