%I
%S 1,2,3,5,6,7,10,11,14,17,19,21,22,23,31,34,38,41,42,46,53,57,59,62,67,
%T 82,83,97,103,106,109,114,115,118,127,131,133,134,157,159,166,179,191,
%U 194,206,211,218,227,230,241,254,262,266,277,283,311,314,318,331
%N Squarefree numbers whose prime indices are powers of a common prime number.
%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 systems.
%e 01: {}
%e 02: {{}}
%e 03: {{1}}
%e 05: {{2}}
%e 06: {{},{1}}
%e 07: {{1,1}}
%e 10: {{},{2}}
%e 11: {{3}}
%e 14: {{},{1,1}}
%e 17: {{4}}
%e 19: {{1,1,1}}
%e 21: {{1},{1,1}}
%e 22: {{},{3}}
%e 23: {{2,2}}
%e 31: {{5}}
%e 34: {{},{4}}
%e 38: {{},{1,1,1}}
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],SameQ@@Join@@primeMS/@primeMS[#]&&SquareFreeQ[#]&]
%Y Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A047966, A281113, A296134, A301766, A302242, A302243.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 10 2018
