A366142 - OEIS

%I #84 Mar 11 2025 07:12:58

%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_ and _Loïc Apothéloz_, Sep 30 2023