A302505 - OEIS

%I #4 Apr 10 2018 21:48:30

%S 1,2,3,4,5,6,8,10,11,12,13,15,16,17,20,22,24,26,29,30,31,32,33,34,40,

%T 41,43,44,47,48,51,52,55,58,59,60,62,64,66,67,68,73,79,80,82,83,85,86,

%U 88,93,94,96,101,102,104,109,110,113,116,118,120,123,124,127

%N Numbers whose prime indices are squarefree and have disjoint prime indices.

%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 multisystems.

%e 01: {}

%e 02: {{}}

%e 03: {{1}}

%e 04: {{},{}}

%e 05: {{2}}

%e 06: {{},{1}}

%e 08: {{},{},{}}

%e 10: {{},{2}}

%e 11: {{3}}

%e 12: {{},{},{1}}

%e 13: {{1,2}}

%e 15: {{1},{2}}

%e 16: {{},{},{},{}}

%e 17: {{4}}

%e 20: {{},{},{2}}

%e 22: {{},{3}}

%e 24: {{},{},{},{1}}

%e 26: {{},{1,2}}

%e 29: {{1,3}}

%e 30: {{},{1},{2}}

%e 31: {{5}}

%e 32: {{},{},{},{},{}}

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],UnsameQ@@Join@@primeMS/@primeMS[#]&]

%Y Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279790, A281113, A294788, A301750, A302242, A302243.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 09 2018