cp's OEIS Frontend

A302591 One, powers of 2, and prime numbers of squarefree index.

%I A302591 #9 Aug 27 2018 01:53:26
%S A302591 1,2,3,4,5,8,11,13,16,17,29,31,32,41,43,47,59,64,67,73,79,83,101,109,
%T A302591 113,127,128,137,139,149,157,163,167,179,181,191,199,211,233,241,256,
%U A302591 257,269,271,277,283,293,313,317,331,347,349,353,367,373,389,397,401
%N A302591 One, powers of 2, and prime numbers of squarefree index.
%C A302591 A prime index of n is a number m such that prime(m) divides n.
%H A302591 Andrew Howroyd, <a href="/A302591/b302591.txt">Table of n, a(n) for n = 1..1000</a>
%F A302591 Union of A000079 and A302491. - _Andrew Howroyd_, Aug 26 2018
%e A302591 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
%e A302591 01: {}
%e A302591 02: {{}}
%e A302591 03: {{1}}
%e A302591 04: {{},{}}
%e A302591 05: {{2}}
%e A302591 08: {{},{},{}}
%e A302591 11: {{3}}
%e A302591 13: {{1,2}}
%e A302591 16: {{},{},{},{}}
%e A302591 17: {{4}}
%e A302591 29: {{1,3}}
%e A302591 31: {{5}}
%e A302591 32: {{},{},{},{},{}}
%e A302591 41: {{6}}
%e A302591 43: {{1,4}}
%e A302591 47: {{2,3}}
%e A302591 59: {{7}}
%e A302591 64: {{},{},{},{},{},{}}
%t A302591 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A302591 Select[Range[400],Or[#===1,Union[primeMS[#]]==={1},PrimeQ[#]&&SquareFreeQ[PrimePi[#]]]&]
%o A302591 (PARI) ok(n)={n>>valuation(n,2) == 1 || (isprime(n) && issquarefree(primepi(n)))} \\ _Andrew Howroyd_, Aug 26 2018
%Y A302591 Cf. A000079, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279791, A281113, A296133, A301765, A302242, A302243, A302491.
%K A302591 nonn
%O A302591 1,2
%A A302591 _Gus Wiseman_, Apr 10 2018