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%I #7 Apr 08 2018 20:09:56
%S 30,70,154,165,210,273,286,330,390,442,462,510,546,561,570,595,646,
%T 690,714,741,770,858,870,874,910,930,1045,1110,1122,1155,1173,1190,
%U 1230,1254,1290,1326,1330,1334,1365,1410,1430,1482,1495,1590,1610,1653,1770
%N Heinz numbers of strict non-knapsack partitions. Squarefree numbers such that more than one divisor has the same Heinz weight A056239(d).
%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).
%F Complement of A005117 in A299702.
%e Sequence of strict non-knapsack partitions begins: (321), (431), (541), (532), (4321), (642), (651), (5321), (6321), (761), (5421), (7321), (6421), (752), (8321), (743), (871), (9321), (7421), (862), (5431), (6521).
%t wt[n_]:=If[n===1,0,Total[Cases[FactorInteger[n],{p_,k_}:>k*PrimePi[p]]]];
%t Select[Range[1000],SquareFreeQ[#]&&!UnsameQ@@wt/@Divisors[#]&]
%Y Cf. A000712, A005117, A056239, A108917, A112798, A122768, A275972, A276024, A284640, A296150, A299701, A299702, A299729, A301829, A301854, A301899.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 28 2018
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