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A317713 Number of distinct terminal subtrees of the rooted tree with Matula-Goebel number n. 36
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = 1+A324923(n). - Antti Karttunen, Oct 23 2023
EXAMPLE
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.
See also illustrations in A061773.
MATHEMATICA
ids[n_]:=Union@@FixedPointList[Union@@(Cases[If[#==1, {}, FactorInteger[#]], {p_, _}:>PrimePi[p]]&/@#)&, {n}];
Table[Length[ids[n]], {n, 100}]
PROG
(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
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
A317713(n) = (1+A324923(n)); \\ Antti Karttunen, Oct 23 2023
CROSSREFS
One more than A324923.
Sequence in context: A286597 A358667 A358552 * A341041 A361660 A318046
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
EXTENSIONS
Data section extended up to a(108) by Antti Karttunen, Oct 23 2023
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)