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 A292886 Number of knapsack factorizations of n. 26
 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, 5, 1, 6, 2, 2, 2, 8, 1, 2, 2, 7, 1, 5, 1, 4, 4, 2, 1, 11, 2, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 11, 1, 2, 4, 7, 2, 5, 1, 4, 2, 5, 1, 15, 1, 2, 4, 4, 2, 5, 1, 11, 4, 2, 1, 11, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A knapsack factorization is a finite multiset of positive integers greater than one such that every distinct submultiset has a different product. The sequence giving the number of factorizations of n is described as "the multiplicative partition function" (see A001055), so knapsack factorizations are a multiplicative generalization of knapsack partitions. - Gus Wiseman, Oct 24 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 EXAMPLE The a(36) = 8 factorizations are 2*2*3*3, 2*2*9, 2*18, 3*3*4, 3*12, 4*9, 6*6, 36. The factorization 2*3*6 is not knapsack. MATHEMATICA postfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[postfacs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[postfacs[n], UnsameQ@@Times@@@Union[Subsets[#]]&]], {n, 100}] CROSSREFS Cf. A001055, A045778, a(p^n) = A108917(n), A162247, A259936, A275972, A281116. Sequence in context: A319685 A034836 A316365 * A317508 A323438 A317141 Adjacent sequences:  A292883 A292884 A292885 * A292887 A292888 A292889 KEYWORD nonn AUTHOR Gus Wiseman, Sep 26 2017 STATUS approved

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Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)