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A299702 Heinz numbers of knapsack partitions. 100

%I #6 Feb 23 2018 11:11:02

%S 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,

%T 29,31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,

%U 56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76,77,78

%N Heinz numbers of knapsack partitions.

%C 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).

%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, A299729.

%K nonn

%O 1,2

%A _Gus Wiseman_, Feb 17 2018

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