%I #8 Apr 11 2018 02:55:17
%S 1,2,3,4,5,8,9,11,16,17,25,27,31,32,41,59,64,67,81,83,109,121,125,127,
%T 128,157,179,191,211,241,243,256,277,283,289,331,353,367,401,431,461,
%U 509,512,547,563,587,599,617,625,709,729,739,773,797,859,877,919
%N Numbers that are powers of a prime number whose prime index is either 1 or also a prime number.
%C A prime index of n is a number m such that prime(m) divides n.
%e 25 is in the sequence because 25 = prime(3)^2 and 3 is a prime number.
%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 04: {{},{}}
%e 05: {{2}}
%e 08: {{},{},{}}
%e 09: {{1},{1}}
%e 11: {{3}}
%e 16: {{},{},{},{}}
%e 17: {{4}}
%e 25: {{2},{2}}
%e 27: {{1},{1},{1}}
%e 31: {{5}}
%e 32: {{},{},{},{},{}}
%e 41: {{6}}
%e 59: {{7}}
%e 64: {{},{},{},{},{},{}}
%e 67: {{8}}
%e 81: {{1},{1},{1},{1}}
%e 83: {{9}}
%t Select[Range[1000],#===1||MatchQ[FactorInteger[#],{{_?(#===2||PrimeQ[PrimePi[#]]&),_}}]&]
%o (PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && ((p==2) || isprime(primepi(p)))); \\ _Michel Marcus_, Apr 10 2018
%Y Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 10 2018