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%I #5 Feb 23 2018 11:11:07
%S 12,24,30,36,40,48,60,63,70,72,80,84,90,96,108,112,120,126,132,140,
%T 144,150,154,156,160,165,168,180,189,192,198,200,204,210,216,220,224,
%U 228,240,252,264,270,273,276,280,286,288,300,308,312,315,320,324,325
%N Heinz numbers of non-knapsack partitions.
%C 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).
%e 12 is the Heinz number of (2,1,1) which is not knapsack because 2 = 1 + 1.
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],!UnsameQ@@Plus@@@Union[Rest@Subsets[primeMS[#]]]&]
%Y Cf. A056239, A108917, A112798, A275972, A276024, A284640, A296150, A299701, A299702.
%K nonn
%O 1,1
%A _Gus Wiseman_, Feb 17 2018
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