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 A326018 Heinz numbers of knapsack partitions such that no addition of one part up to the maximum is knapsack. 6
 1925, 12155, 20995, 23375, 37145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS EXAMPLE 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} MATHEMATICA 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]=={}]&] CROSSREFS Cf. A002033, A108917, A275972, A299702, A299729, A304793. Cf. A325780, A325782, A325857, A325862, A325878, A325880, A326015, A326016. Sequence in context: A107564 A135648 A255867 * A202051 A283949 A133301 Adjacent sequences:  A326015 A326016 A326017 * A326019 A326020 A326021 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 03 2019 STATUS approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)