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A293627
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Number of knapsack factorizations whose factors sum to n.
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11
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1, 1, 1, 2, 2, 4, 4, 6, 8, 11, 12, 19, 21, 27, 34, 45, 51, 69, 77, 100, 117, 146
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OFFSET
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1,4
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COMMENTS
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A knapsack factorization is a finite multiset of positive integers greater than one such that every distinct submultiset has a different product.
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LINKS
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EXAMPLE
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The a(12) = 19 partitions are:
(12),
(10 2), (9 3), (8 4), (7 5), (6 6),
(8 2 2), (7 3 2), (6 4 2), (6 3 3), (5 5 2), (5 4 3), (4 4 4),
(6 2 2 2), (5 3 2 2), (4 3 3 2), (3 3 3 3),
(3 3 2 2 2),
(2 2 2 2 2 2).
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MATHEMATICA
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nn=22;
apsQ[y_]:=UnsameQ@@Times@@@Union[Rest@Subsets[y]];
Table[Length@Select[IntegerPartitions[n], apsQ], {n, nn}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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