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%I #8 Apr 08 2018 20:10:08
%S 0,1,1,2,1,3,1,10,2,3,1,21,1,3,3,58,1,21,1,21,3,3,1,164,2,3,10,21,1,
%T 34,1,373,3,3,3,218,1,3,3,161,1,7,1,5,5,3,1,1320,2,5,3,5,1,7,3,7,3,3,
%U 1,7,1,3,4,2558,3,7,1,5,3,6,1,7
%N Number of positive subset-sum trees whose composite a positive subset-sum of the integer partition with Heinz number n.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A positive subset-sum tree with root x is either the symbol x itself, or is obtained by first choosing a positive subset-sum x <= (y_1,...,y_k) with k > 1 and then choosing a positive subset-sum tree with root y_i for each i = 1...k. The composite of a positive subset-sum tree is the positive subset-sum x <= g where x is the root sum and g is the multiset of leaves. We write positive subset-sum trees in the form rootsum(branch,...,branch). For example, 4(1(1,3),2,2(1,1)) is a positive subset-sum tree with composite 4(1,1,1,2,3) and weight 8.
%H Gus Wiseman, <a href="/A301935/a301935.png">The a(12) = 21 positive subset-sum trees.</a>
%Y Cf. A000108, A000712, A108917, A122768, A262671, A262673, A275972, A276024, A284640, A299701, A301854, A301855, A301856, A301934.
%K nonn
%O 1,4
%A _Gus Wiseman_, Mar 28 2018
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