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%I #77 Oct 05 2023 08:35:27
%S 1,2,3,4,5,7,8,9,11,12,16,17,18,19,20,23,25,27,28,31,32,36,37,44,45,
%T 48,49,50,53,59,61,63,64,67,68,71,72,75,76,80,81,83,92,97,98,99,100,
%U 103,107,108,112,121,124,125,127,128,131,144,147,148,151,153,157,162,169,171,175,176,180
%N Matula-Goebel numbers of rooted trees which are symmetrical about a straight line passing through the root.
%C The Matula-Goebel number of a tree is Product prime(k_i), where the k_i are the Matula-Goebel numbers of the child subtrees of the root.
%C A tree is symmetric about a line iff the root has 2 copies of each child subtree (one each side of the line), and an optional "middle" child subtree on the line and in turn symmetric too.
%H Ramzan Guekhaev, <a href="https://docs.google.com/document/d/1Jw9gCVk9xGeHbuXoEKlj_X2lCXFFZLHjA8zVrGDSpnU/edit?usp=sharing">Flowery numbers.docx</a>.
%H Ramzan Guekhaev, <a href="https://docs.google.com/document/d/1b-OuKxIZkuoftma9n6ad3Y5BrElAwcM6uxK7SuKk2iM/edit?usp=drivesdk">Table for n, a(n) for n = 1..455</a>
%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F a(1) = 1; k > 1 is a term iff (k/p^2 is a term for some p) OR (k = prime(j) where j is a term).
%e 12 is a term since it's the Matula-Goebel number of the following tree which is, per the layout shown, symmetric about the vertical.
%e (*)
%e |
%e (*) (*) (*)
%e \ | /
%e \ | /
%e (*) root
%Y Cf. A000040.
%K nonn
%O 1,2
%A _Ramzan Guekhaev_, Sep 30 2023
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