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| NAME
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allocatedHeinz numbers of knapsack partitions such that no addition of one part up to the formaximum Gusis Wisemanknapsack.
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| DATA
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1925, 12155, 20995, 23375, 37145
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| OFFSET
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1,1
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| COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
An integer partition is knapsack if every submultiset has a different sum.
The enumeration of these partitions by sum is given by A326016.
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| EXAMPLE
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The sequence of terms together with their prime indices begins:
1925: {3,3,4,5}
12155: {3,5,6,7}
20995: {3,6,7,8}
23375: {3,3,3,5,7}
37145: {3,7,8,9}
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| MATHEMATICA
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ksQ[y_]:=UnsameQ@@Total/@Union[Subsets[y]];
Select[Range[2, 200], With[{phm=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, ksQ[phm]&&Select[Table[Sort[Append[phm, i]], {i, Max@@phm}], ksQ]=={}]&]
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| CROSSREFS
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Cf. A002033, A108917, A275972, A299702, A299729, A304793.
Cf. A325780, A325782, A325857, A325862, A325878, A325880, A326015, A326016.
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| KEYWORD
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allocated
nonn,more
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| AUTHOR
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Gus Wiseman, Jun 03 2019
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| STATUS
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approved
editing
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