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 A301935 Number of positive subset-sum trees whose composite a positive subset-sum of the integer partition with Heinz number n. 6
 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, 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, 1, 7, 1, 3, 4, 2558, 3, 7, 1, 5, 3, 6, 1, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. LINKS Gus Wiseman, The a(12) = 21 positive subset-sum trees. CROSSREFS Cf. A000108, A000712, A108917, A122768, A262671, A262673, A275972, A276024, A284640, A299701, A301854, A301855, A301856, A301934. Sequence in context: A126761 A090559 A186725 * A237978 A098570 A122048 Adjacent sequences:  A301932 A301933 A301934 * A301936 A301937 A301938 KEYWORD nonn AUTHOR Gus Wiseman, Mar 28 2018 STATUS approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)