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Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n.
36

%I #14 Oct 23 2023 11:47:13

%S 1,2,3,2,4,3,3,2,3,4,5,3,4,3,4,2,4,3,3,4,4,5,4,3,4,4,3,3,5,4,6,2,5,4,

%T 5,3,4,3,4,4,5,4,4,5,4,4,5,3,3,4,5,4,3,3,5,3,4,5,5,4,4,6,4,2,5,5,4,4,

%U 4,5,5,3,5,4,4,3,6,4,6,4,3,5,5,4,6,4,5,5,4,4,5,4,6,5,5,3,5,3,5,4,5,5,4,4,5,3,4,3

%N Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n.

%H Antti Karttunen, <a href="/A317713/b317713.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Göbel numbers</a>

%F a(n) = 1+A324923(n). - _Antti Karttunen_, Oct 23 2023

%e 20 is the Matula-Goebel number of the tree (oo((o))), which has 4 distinct terminal subtrees: {(oo((o))), ((o)), (o), o}. So a(20) = 4.

%e See also illustrations in A061773.

%t ids[n_]:=Union@@FixedPointList[Union@@(Cases[If[#==1,{},FactorInteger[#]],{p_,_}:>PrimePi[p]]&/@#)&,{n}];

%t Table[Length[ids[n]],{n,100}]

%o (PARI)

%o A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);

%o A324923(n) = { my(lista = List([]), gpf, i); while(n > 1, gpf=A006530(n); i = primepi(gpf); n /= gpf; n *= i; listput(lista,i)); #Set(lista); }; \\ _Antti Karttunen_, Oct 23 2023

%o A317713(n) = (1+A324923(n)); \\ _Antti Karttunen_, Oct 23 2023

%Y One more than A324923.

%Y Cf. A000081, A007097, A049076, A061773, A061775, A076146, A109082, A109129, A206491, A303431, A316476.

%K nonn

%O 1,2

%A _Gus Wiseman_, Aug 05 2018

%E Data section extended up to a(108) by _Antti Karttunen_, Oct 23 2023