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 A299729 Heinz numbers of non-knapsack partitions. 34
 12, 24, 30, 36, 40, 48, 60, 63, 70, 72, 80, 84, 90, 96, 108, 112, 120, 126, 132, 140, 144, 150, 154, 156, 160, 165, 168, 180, 189, 192, 198, 200, 204, 210, 216, 220, 224, 228, 240, 252, 264, 270, 273, 276, 280, 286, 288, 300, 308, 312, 315, 320, 324, 325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS An integer partition is non-knapsack if there exist two different submultisets with the same 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..54. EXAMPLE 12 is the Heinz number of (2,1,1) which is not knapsack because 2 = 1 + 1. 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, A299702. Sequence in context: A334760 A098714 A334758 * A325777 A364532 A350056 Adjacent sequences: A299726 A299727 A299728 * A299730 A299731 A299732 KEYWORD nonn AUTHOR Gus Wiseman, Feb 17 2018 STATUS approved

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Last modified September 15 13:23 EDT 2024. Contains 375938 sequences. (Running on oeis4.)