cp's OEIS Frontend

A302534 Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices.

%I A302534 #5 Apr 10 2018 21:48:44
%S A302534 1,2,3,5,6,10,11,13,15,17,22,26,29,30,31,33,34,41,43,47,51,55,58,59,
%T A302534 62,66,67,73,79,82,83,85,86,93,94,101,102,109,110,113,118,123,127,134,
%U A302534 137,139,141,143,145,146,149,155,157,158,163,165,166,167,170,177
%N A302534 Squarefree numbers whose prime indices are also squarefree and have disjoint prime indices.
%C A302534 A prime index of n is a number m such that prime(m) divides n.
%e A302534 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
%e A302534 01: {}
%e A302534 02: {{}}
%e A302534 03: {{1}}
%e A302534 05: {{2}}
%e A302534 06: {{},{1}}
%e A302534 10: {{},{2}}
%e A302534 11: {{3}}
%e A302534 13: {{1,2}}
%e A302534 15: {{1},{2}}
%e A302534 17: {{4}}
%e A302534 22: {{},{3}}
%e A302534 26: {{},{1,2}}
%e A302534 29: {{1,3}}
%e A302534 30: {{},{1},{2}}
%e A302534 31: {{5}}
%e A302534 33: {{1},{3}}
%e A302534 34: {{},{4}}
%e A302534 41: {{6}}
%e A302534 43: {{1,4}}
%e A302534 47: {{2,3}}
%e A302534 51: {{1},{4}}
%e A302534 55: {{2},{3}}
%e A302534 58: {{},{1,3}}
%e A302534 59: {{7}}
%e A302534 62: {{},{5}}
%e A302534 66: {{},{1},{3}}
%t A302534 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A302534 Select[Range[100],SquareFreeQ[#]&&UnsameQ@@Join@@primeMS/@primeMS[#]&]
%Y A302534 Cf. A000009, A000961, A001222, A003963, A005117, A007359, A007716, A051424, A056239, A275024, A279375, A281113, A289509, A294786, A301756, A302242, A302243, A302505, A302521.
%K A302534 nonn
%O A302534 1,2
%A A302534 _Gus Wiseman_, Apr 09 2018