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Numbers whose multiset of prime factors is not knapsack.
1

%I #6 Jun 06 2018 18:33:11

%S 30,60,70,72,84,90,120,140,144,150,168,180,210,216,240,252,270,280,

%T 286,288,300,308,330,336,350,360,378,390,420,432,440,450,480,490,495,

%U 504,510,525,528,540,560,570,572,576,588,594,600,616,630,646,648,660,672

%N Numbers whose multiset of prime factors is not knapsack.

%C A multiset of positive integers is knapsack if every distinct submultiset has a different sum.

%e 30 = 2 * 3 * 5 is not knapsack because 2 + 3 = 5.

%t Select[Range[1000],DivisorSigma[0,#]=!=Length[Union[Total/@Subsets[Join@@Cases[FactorInteger[#],{p_,k_}:>Table[p,{k}]]]]]&]

%Y Cf. A027746, A108917, A122768, A275972, A276024, A299701, A299729, A301855, A301900, A304793, A305611.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 06 2018