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.
%I A038991 #59 Apr 12 2025 01:40:49
%S A038991 1,15,40,155,156,600,400,1395,1210,2340,1464,6200,2380,6000,6240,
%T A038991 11811,5220,18150,7240,24180,16000,21960,12720,55800,20306,35700,
%U A038991 33880,62000,25260,93600,30784,97155,58560,78300,62400,187550,52060,108600,95200,217620,70644,240000,81400
%N A038991 Number of sublattices of index n in generic 4-dimensional lattice.
%D A038991 M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
%H A038991 Amiram Eldar, <a href="/A038991/b038991.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from G. C. Greubel)
%H A038991 M. Baake and U. Grimm, <a href="http://arXiv.org/abs/math-ph/0212015">Combinatorial problems of (quasi)crystallography</a>, arXiv:math-ph/0212015, 2002.
%H A038991 M. Baake and N. Neumarker, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Baake/baake7.html">A Note on the Relation Between Fixed Point and Orbit Count Sequences</a>, JIS 12 (2009) 09.4.4, Section 3.
%H A038991 Tad White, <a href="http://arxiv.org/abs/1304.2830">Counting Free Abelian Actions</a>, arXiv preprint arXiv:1304.2830 [math.CO], 2013.
%H A038991 <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>
%F A038991 f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=4.
%F A038991 Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)*zeta(s-3).
%F A038991 Dirichlet convolution of A000578 and A001001.
%F A038991 Multiplicative with a(p^e) = Product_{k=1..3} (p^(e+k)-1)/(p^k-1).
%F A038991 Sum_{k=1..n} a(k) ~ Pi^6 * Zeta(3) * n^4 / 2160. - _Vaclav Kotesovec_, Feb 01 2019
%F A038991 Conjectured g.f.: Sum_{k>=1} Sum {l>=1} Sum {m>=1} k*l^2*m^3*x^(k*l*m)/(1 - x^(k*l*m)) (by extension of g.f for A001001). - _Miles Wilson_, Apr 05 2025
%t A038991 a[n_] := DivisorSum[n, #*DivisorSum[#, #*DivisorSum[#, #&]&]&]; Array[a, 50] (* _Jean-François Alcover_, Dec 02 2015, after _Joerg Arndt_ *)
%t A038991 f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 3}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)
%o A038991 (PARI) a(n)=sumdiv(n,x, x * sumdiv(x,y, y * sumdiv(y,z, z ) ) ); /* _Joerg Arndt_, Oct 07 2012 */
%Y A038991 Column 4 of A160870.
%Y A038991 Cf. A001001, A038992, A038993, A038994, A038995, A038996, A038997, A038998, A038999.
%K A038991 nonn,mult
%O A038991 1,2
%A A038991 _N. J. A. Sloane_
%E A038991 Offset changed from 0 to 1 by _R. J. Mathar_, Mar 31 2011
%E A038991 More terms from _Joerg Arndt_, Oct 07 2012