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%I #4 Apr 10 2018 21:48:37
%S 1,3,5,11,13,15,17,29,31,33,41,43,47,51,55,59,67,73,79,83,85,93,101,
%T 109,113,123,127,137,139,141,143,145,149,155,157,163,165,167,177,179,
%U 181,187,191,199,201,205,211,215,219,221,233,241,249,255,257,269,271
%N Odd numbers whose prime indices are squarefree and have disjoint prime indices. Numbers n such that the n-th multiset multisystem is a set partition.
%C A prime index of n is a number m such that prime(m) divides n.
%e Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set partitions.
%e 01: {}
%e 03: {{1}}
%e 05: {{2}}
%e 11: {{3}}
%e 13: {{1,2}}
%e 15: {{1},{2}}
%e 17: {{4}}
%e 29: {{1,3}}
%e 31: {{5}}
%e 33: {{1},{3}}
%e 41: {{6}}
%e 43: {{1,4}}
%e 47: {{2,3}}
%e 51: {{1},{4}}
%e 55: {{2},{3}}
%e 59: {{7}}
%e 67: {{8}}
%e 73: {{2,4}}
%e 79: {{1,5}}
%e 83: {{9}}
%e 85: {{2},{4}}
%e 93: {{1},{5}}
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[1,100,2],UnsameQ@@Join@@primeMS/@primeMS[#]&]
%Y Cf. A000110, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279790, A281113, A294788, A301750, A302242, A302243, A302505.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 09 2018
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