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%I #8 Apr 21 2018 20:58:17
%S 18,36,42,45,50,54,72,75,78,84,90,98,99,100,105,108,114,126,130,135,
%T 144,150,153,156,162,168,174,175,180,182,195,196,198,200,207,210,216,
%U 222,225,228,230,231,234,242,245,250,252,258,260,266,270,275,279,285,288
%N Numbers whose prime indices have no common divisor other than 1 but are not pairwise coprime.
%C A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair of them has a common divisor other than 1.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e The sequence of integer partitions whose Heinz numbers belong to this sequence begins (221), (2211), (421), (322), (331), (2221), (22111), (332), (621), (4211), (3221), (441), (522), (3311), (432), (22211).
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[400],!CoprimeQ@@primeMS[#]&&GCD@@primeMS[#]===1&]
%Y Cf. A000837, A001222, A018783, A051424, A056239, A078374, A168532, A289508, A289509, A296150, A298748, A300486, A302569, A302696, A302796, A303138, A303139, A303140, A303283.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 20 2018