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 A299702 Heinz numbers of knapsack partitions. 91
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS An integer partition is knapsack if every distinct submultiset has a different sum. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS Table of n, a(n) for n=1..68. MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], UnsameQ@@Plus@@@Union[Rest@Subsets[primeMS[#]]]&] CROSSREFS Cf. A056239, A108917, A112798, A275972, A276024, A284640, A296150, A299701, A299729. Sequence in context: A160453 A325778 A364531 * A348577 A361232 A027855 Adjacent sequences: A299699 A299700 A299701 * A299703 A299704 A299705 KEYWORD nonn AUTHOR Gus Wiseman, Feb 17 2018 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)