OFFSET
1,3
COMMENTS
An unlabeled rooted tree is uniform and relatively prime iff either it is a single node or a single node with a single uniform relatively prime branch, or the branches of the root have empty intersection (relatively prime) and equal multiplicities (uniform) and are themselves uniform relatively prime trees.
LINKS
A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp. 1-12.
EXAMPLE
The a(6) = 13 uniform relatively prime rooted trees:
(((((o)))))
((((oo))))
(((o(o))))
(((ooo)))
((o((o))))
((o(oo)))
((oooo))
(o(((o))))
(o((oo)))
(o(o(o)))
(o(ooo))
((o)((o)))
(ooooo)
MATHEMATICA
purt[n_]:=purt[n]=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[purt/@ptn]], Or[Length[#]==1, And[SameQ@@Length/@Split[#], Intersection@@#=={}]]&], {ptn, IntegerPartitions[n-1]}]];
Table[Length[purt[n]], {n, 20}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved