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A317713 Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n.

%I A317713 #14 Oct 23 2023 11:47:13
%S A317713 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 A317713 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 A317713 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 A317713 Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n.
%H A317713 Antti Karttunen, <a href="/A317713/b317713.txt">Table of n, a(n) for n = 1..16384</a>
%H A317713 <a href="/index/Mat#matula">Index entries for sequences related to Matula-Göbel numbers</a>
%F A317713 a(n) = 1+A324923(n). - _Antti Karttunen_, Oct 23 2023
%e A317713 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 A317713 See also illustrations in A061773.
%t A317713 ids[n_]:=Union@@FixedPointList[Union@@(Cases[If[#==1,{},FactorInteger[#]],{p_,_}:>PrimePi[p]]&/@#)&,{n}];
%t A317713 Table[Length[ids[n]],{n,100}]
%o A317713 (PARI)
%o A317713 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A317713 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 A317713(n) = (1+A324923(n)); \\ _Antti Karttunen_, Oct 23 2023
%Y A317713 One more than A324923.
%Y A317713 Cf. A000081, A007097, A049076, A061773, A061775, A076146, A109082, A109129, A206491, A303431, A316476.
%K A317713 nonn
%O A317713 1,2
%A A317713 _Gus Wiseman_, Aug 05 2018
%E A317713 Data section extended up to a(108) by _Antti Karttunen_, Oct 23 2023