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A317708 Number of aperiodic relatively prime trees with n nodes. 15
1, 1, 1, 2, 4, 10, 20, 48, 108, 255, 595, 1435, 3434, 8372, 20419, 50289, 124289, 309122, 771508, 1934462 (list; graph; refs; listen; history; text; internal format)



An unlabeled rooted tree is aperiodic and relatively prime iff either it is a single node or a single node with a single aperiodic relatively prime branch, or the branches directly under any given node have empty intersection (relatively prime) and also have relatively prime multiplicities (aperiodic) and are themselves aperiodic relatively prime trees.


Table of n, a(n) for n=1..20.

Gus Wiseman, All 48 aperiodic relatively prime trees with 8 nodes.


The a(6) = 10 aperiodic relatively prime trees:












rurt[n_]:=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[rurt/@ptn]], Or[Length[#]==1, And[Intersection@@#=={}, GCD@@Length/@Split[#]==1]]&], {ptn, IntegerPartitions[n-1]}]];

Table[Length[rurt[n]], {n, 10}]


Cf. A000081, A001190, A004111, A301700, A303431, A316501, A316500.

Cf. A317705, A317707, A317709, A317710, A317711, A317712.

Sequence in context: A232466 A003407 A151523 * A265264 A026395 A247630

Adjacent sequences:  A317705 A317706 A317707 * A317709 A317710 A317711




Gus Wiseman, Aug 05 2018



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Last modified December 5 20:54 EST 2019. Contains 329779 sequences. (Running on oeis4.)