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A302597 Squarefree numbers whose prime indices are powers of a common prime number. 0

%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

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Last modified September 21 15:50 EDT 2020. Contains 337272 sequences. (Running on oeis4.)