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.

A038995 Number of sublattices of index n in generic 8-dimensional lattice.

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%I A038995 #27 May 08 2023 21:50:06
%S A038995 1,255,3280,43435,97656,836400,960800,6347715,8069620,24902280,
%T A038995 21435888,142466800,67977560,245004000,320311680,866251507,435984840,
%U A038995 2057753100,943531280,4241688360,3151424000,5466151440,3559590240,20820505200,7947261556,17334277800,18326727760
%N A038995 Number of sublattices of index n in generic 8-dimensional lattice.
%D A038995 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 A038995 Amiram Eldar, <a href="/A038995/b038995.txt">Table of n, a(n) for n = 1..10000</a>
%H A038995 <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>
%F A038995 f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=8.
%F A038995 Multiplicative with a(p^e) = Product_{k=1..7} (p^(e+k)-1)/(p^k-1).
%F A038995 Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k). - _R. J. Mathar_, Apr 01 2011
%F A038995 Sum_{k=1..n} a(k) ~ c * n^8, where c = Pi^20*zeta(3)*zeta(5)*zeta(7)/43401015000 = 0.285716... . - _Amiram Eldar_, Oct 19 2022
%t A038995 f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 7}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)
%Y A038995 Column 8 of A160870.
%Y A038995 Cf. A001001, A038991, A038992, A038993, A038994, A038996, A038997, A038998, A038999.
%K A038995 nonn,mult
%O A038995 1,2
%A A038995 _N. J. A. Sloane_
%E A038995 Offset set to 1 by _R. J. Mathar_, Mar 01 2011
%E A038995 More terms from _Amiram Eldar_, Aug 29 2019