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 A177821 #29 Mar 30 2025 15:37:02
%S A177821 1,1,1,3,3,3,6,6,8,12,14,18,23,27,34,43,52,62,79,93,109,138,159,187,
%T A177821 236,270,316,385,442,517,619,716,833,980,1132,1308,1533,1758,2027,
%U A177821 2370,2703,3095,3594,4081,4668,5397,6125,6970,8007,9065,10281,11753,13289,15036,17120,19305,21788,24690,27768,31294,35381,39690,44591,50261,56267,63047
%N A177821 a(n) gives the number of nonisomorphic connected compact Lie groups of dimension n which are simple products.
%C A177821 By the structure theorem for compact Lie groups, every compact connected Lie group is a finite central quotient of a product of copies of the circle group U(1) and compact simple Lie groups which are all known due to Cartan's classification. This sequence counts only those which are direct products of such groups.
%F A177821 G.f.: 1/((1-x)*(1-x^3)^2*(1-x^8)^2*(1-x^10)^2*(1-x^14)*...) = (1/(1-x)) * Product_{k>=0} (1-x^k)^A178176(k) with (1-x^k)^0 taken to be 1.
%e A177821 For n=0, the trivial group is the only such group.
%e A177821 For n=8, the 8 Lie groups are U(1)^8, U(1)^5 x SU(2), U(1)^5 x SO(3), U(1)^2 x SU(2)^2, U(1)^2 x SU(2) x SO(3), U(1)^2 x SO(3)^2, SU(3) and SU(3)/3.
%Y A177821 See also A178176 for enumeration of the simple factors giving these counts.
%K A177821 nonn
%O A177821 0,4
%A A177821 _Andrew Rupinski_, Dec 18 2010
%E A177821 a(28) and following corrected by _Andrea Aveni_, Mar 22 2025