A302601 - OEIS

%I #8 Apr 11 2018 02:55:10

%S 1,3,5,7,9,11,17,19,23,25,27,31,41,49,53,59,67,81,83,97,103,109,121,

%T 125,127,131,157,179,191,211,227,241,243,277,283,289,311,331,343,353,

%U 361,367,401,419,431,461,509,529,547,563,587,599,617,625,661,691,709

%N Numbers that are powers of a prime number whose prime index is also a prime power (not including 1).

%C A prime index of n is a number m such that prime(m) divides n.

%e 49 is in the sequence because 49 = prime(4)^2 = prime(prime(1)^2)^2.

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

%e 001: {}

%e 003: {{1}}

%e 005: {{2}}

%e 007: {{1,1}}

%e 009: {{1},{1}}

%e 011: {{3}}

%e 017: {{4}}

%e 019: {{1,1,1}}

%e 023: {{2,2}}

%e 025: {{2},{2}}

%e 027: {{1},{1},{1}}

%e 031: {{5}}

%e 041: {{6}}

%e 049: {{1,1},{1,1}}

%e 053: {{1,1,1,1}}

%e 059: {{7}}

%e 067: {{8}}

%e 081: {{1},{1},{1},{1}}

%e 083: {{9}}

%e 097: {{3,3}}

%e 103: {{2,2,2}}

%e 109: {{10}}

%e 121: {{3},{3}}

%e 125: {{2},{2},{2}}

%e 127: {{11}}

%e 131: {{1,1,1,1,1}}

%t Select[Range[1000],#===1||MatchQ[FactorInteger[#],{{_?(PrimePowerQ[PrimePi[#]]&),_}}]&]

%o (PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && isprimepower(primepi(p))); \\ _Michel Marcus_, Apr 10 2018

%Y Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243, A302498.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 10 2018