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%I #8 Jul 28 2023 15:54:50
%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 29,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,
%U 55,56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,75,76
%N Positive integers such that if prime(a)*prime(b) is a divisor, prime(a+b) is not.
%C Also Heinz numbers of a type of sum-free partitions not allowing re-used parts, counted by A236912.
%e The prime indices of 198 are {1,2,2,5}, which is sum-free even though it is not knapsack (A299702, A299729), so 198 is in the sequence.
%t prix[n_]:=If[n==1,{}, Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],Intersection[prix[#], Total/@Subsets[prix[#],{2}]]=={}&]
%Y Subsets of this type are counted by A085489, with re-usable parts A007865.
%Y Subsets not of this type are counted by A093971, w/ re-usable parts A088809.
%Y Partitions of this type are counted by A236912.
%Y Allowing parts to be re-used gives A364347, counted by A364345.
%Y The complement allowing parts to be re-used is A364348, counted by A363225.
%Y The non-binary version allowing re-used parts is counted by A364350.
%Y The complement is A364462, counted by A237113.
%Y The non-binary version is A364531, counted by A237667, complement A364532.
%Y A001222 counts prime indices.
%Y A108917 counts knapsack partitions, ranks A299702.
%Y A112798 lists prime indices, sum A056239.
%Y Cf. A151897, A288728, A320340, A325862, A325864, A326083, A363226, A364346.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 27 2023
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