cp's OEIS Frontend

A302498 Numbers that are a power of a prime number whose prime index is itself a power of a prime number.

%I A302498 #11 Aug 27 2018 01:53:12
%S A302498 1,2,3,4,5,7,8,9,11,16,17,19,23,25,27,31,32,41,49,53,59,64,67,81,83,
%T A302498 97,103,109,121,125,127,128,131,157,179,191,211,227,241,243,256,277,
%U A302498 283,289,311,331,343,353,361,367,401,419,431,461,509,512,529,547,563
%N A302498 Numbers that are a power of a prime number whose prime index is itself a power of a prime number.
%C A302498 A prime index of n is a number m such that prime(m) divides n.
%H A302498 Andrew Howroyd, <a href="/A302498/b302498.txt">Table of n, a(n) for n = 1..1000</a>
%e A302498 49 is in the sequence because 49 = prime(prime(1)^2)^2.
%e A302498 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of constant constant-multiset multisystems.
%e A302498 01: {}
%e A302498 02: {{}}
%e A302498 03: {{1}}
%e A302498 04: {{},{}}
%e A302498 05: {{2}}
%e A302498 07: {{1,1}}
%e A302498 08: {{},{},{}}
%e A302498 09: {{1},{1}}
%e A302498 11: {{3}}
%e A302498 16: {{},{},{},{}}
%e A302498 17: {{4}}
%e A302498 19: {{1,1,1}}
%e A302498 23: {{2,2}}
%e A302498 25: {{2},{2}}
%e A302498 27: {{1},{1},{1}}
%e A302498 31: {{5}}
%e A302498 32: {{},{},{},{},{}}
%e A302498 41: {{6}}
%e A302498 49: {{1,1},{1,1}}
%e A302498 53: {{1,1,1,1}}
%e A302498 59: {{7}}
%e A302498 64: {{},{},{},{},{},{}}
%t A302498 Select[Range[100],Or[#===1,PrimePowerQ[#]&&And@@(Or[#===1,PrimePowerQ[#]]&/@PrimePi/@FactorInteger[#][[All,1]])]&]
%o A302498 (PARI) ok(n)={my(p); n == 1 || (isprimepower(n, &p) && (p == 2 || isprimepower(primepi(p))))} \\ _Andrew Howroyd_, Aug 26 2018
%Y A302498 Cf. A000961, A001222, A003963, A005117, A007716, A056239, A076610, A275024, A279789, A295920, A301763, A302242, A302243, A302492, A302493, A302496, A302497.
%K A302498 nonn
%O A302498 1,2
%A A302498 _Gus Wiseman_, Apr 09 2018