cp's OEIS Frontend

A302592 One, powers of 2, and prime numbers of prime index.

%I A302592 #10 Aug 27 2018 01:53:31
%S A302592 1,2,3,4,5,8,11,16,17,31,32,41,59,64,67,83,109,127,128,157,179,191,
%T A302592 211,241,256,277,283,331,353,367,401,431,461,509,512,547,563,587,599,
%U A302592 617,709,739,773,797,859,877,919,967,991,1024,1031,1063,1087,1153,1171
%N A302592 One, powers of 2, and prime numbers of prime index.
%H A302592 Andrew Howroyd, <a href="/A302592/b302592.txt">Table of n, a(n) for n = 1..1000</a>
%F A302592 Union of A000079 and A006450. - _Andrew Howroyd_, Aug 26 2018
%e A302592 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
%e A302592 001: {}
%e A302592 002: {{}}
%e A302592 003: {{1}}
%e A302592 004: {{},{}}
%e A302592 005: {{2}}
%e A302592 008: {{},{},{}}
%e A302592 011: {{3}}
%e A302592 016: {{},{},{},{}}
%e A302592 017: {{4}}
%e A302592 031: {{5}}
%e A302592 032: {{},{},{},{},{}}
%e A302592 041: {{6}}
%e A302592 059: {{7}}
%e A302592 064: {{},{},{},{},{},{}}
%e A302592 067: {{8}}
%e A302592 083: {{9}}
%e A302592 109: {{10}}
%e A302592 127: {{11}}
%e A302592 128: {{},{},{},{},{},{},{}}
%t A302592 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A302592 Select[Range[1000],Or[#===1,Union[primeMS[#]]==={1},PrimeQ[#]&&PrimeQ[PrimePi[#]]]&]
%o A302592 (PARI) ok(n)={n>>valuation(n,2) == 1 || (isprime(n) && isprime(primepi(n)))} \\ _Andrew Howroyd_, Aug 26 2018
%Y A302592 Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A279791, A281113, A296133, A301765, A302242, A302243.
%K A302592 nonn
%O A302592 1,2
%A A302592 _Gus Wiseman_, Apr 10 2018