cp's OEIS Frontend

A302497 Powers of primes of squarefree index.

%I A302497 #6 Apr 10 2018 21:48:17
%S A302497 1,2,3,4,5,8,9,11,13,16,17,25,27,29,31,32,41,43,47,59,64,67,73,79,81,
%T A302497 83,101,109,113,121,125,127,128,137,139,149,157,163,167,169,179,181,
%U A302497 191,199,211,233,241,243,256,257,269,271,277,283,289,293,313,317,331
%N A302497 Powers of primes of squarefree index.
%C A302497 A prime index of n is a number m such that prime(m) divides n.
%e A302497 49 is not in the sequence because 49 = prime(4)^2 but 4 is not squarefree.
%e A302497 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of constant set multisystems.
%e A302497 01: {}
%e A302497 02: {{}}
%e A302497 03: {{1}}
%e A302497 04: {{},{}}
%e A302497 05: {{2}}
%e A302497 08: {{},{},{}}
%e A302497 09: {{1},{1}}
%e A302497 11: {{3}}
%e A302497 13: {{1,2}}
%e A302497 16: {{},{},{},{}}
%e A302497 17: {{4}}
%e A302497 25: {{2},{2}}
%e A302497 27: {{1},{1},{1}}
%e A302497 29: {{1,3}}
%e A302497 31: {{5}}
%e A302497 32: {{},{},{},{},{}}
%e A302497 41: {{6}}
%e A302497 43: {{1,4}}
%e A302497 47: {{2,3}}
%e A302497 59: {{7}}
%e A302497 64: {{},{},{},{},{},{}}
%t A302497 Select[Range[100],Or[#===1,PrimePowerQ[#]&&And@@SquareFreeQ/@PrimePi/@FactorInteger[#][[All,1]]]&]
%o A302497 (PARI) is(n) = if(n==1, return(1), my(x=isprimepower(n)); if(x > 0, if(issquarefree(primepi(ceil(n^(1/x)))), return(1)))); 0 \\ _Felix Fröhlich_, Apr 10 2018
%Y A302497 Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279788, A281113, A296132, A301768, A302242, A302243, A302478, A302494.
%K A302497 nonn
%O A302497 1,2
%A A302497 _Gus Wiseman_, Apr 09 2018