%I #10 Aug 27 2018 01:53:31

%S 1,2,3,4,5,8,11,16,17,31,32,41,59,64,67,83,109,127,128,157,179,191,

%T 211,241,256,277,283,331,353,367,401,431,461,509,512,547,563,587,599,

%U 617,709,739,773,797,859,877,919,967,991,1024,1031,1063,1087,1153,1171

%N One, powers of 2, and prime numbers of prime index.

%H Andrew Howroyd, <a href="/A302592/b302592.txt">Table of n, a(n) for n = 1..1000</a>

%F Union of A000079 and A006450. - _Andrew Howroyd_, Aug 26 2018

%e Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.

%e 001: {}

%e 002: {{}}

%e 003: {{1}}

%e 004: {{},{}}

%e 005: {{2}}

%e 008: {{},{},{}}

%e 011: {{3}}

%e 016: {{},{},{},{}}

%e 017: {{4}}

%e 031: {{5}}

%e 032: {{},{},{},{},{}}

%e 041: {{6}}

%e 059: {{7}}

%e 064: {{},{},{},{},{},{}}

%e 067: {{8}}

%e 083: {{9}}

%e 109: {{10}}

%e 127: {{11}}

%e 128: {{},{},{},{},{},{},{}}

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[1000],Or[#===1,Union[primeMS[#]]==={1},PrimeQ[#]&&PrimeQ[PrimePi[#]]]&]

%o (PARI) ok(n)={n>>valuation(n,2) == 1 || (isprime(n) && isprime(primepi(n)))} \\ _Andrew Howroyd_, Aug 26 2018

%Y Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A279791, A281113, A296133, A301765, A302242, A302243.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 10 2018