cp's OEIS Frontend

A302601 Numbers that are powers of a prime number whose prime index is also a prime power (not including 1).

%I A302601 #8 Apr 11 2018 02:55:10
%S A302601 1,3,5,7,9,11,17,19,23,25,27,31,41,49,53,59,67,81,83,97,103,109,121,
%T A302601 125,127,131,157,179,191,211,227,241,243,277,283,289,311,331,343,353,
%U A302601 361,367,401,419,431,461,509,529,547,563,587,599,617,625,661,691,709
%N A302601 Numbers that are powers of a prime number whose prime index is also a prime power (not including 1).
%C A302601 A prime index of n is a number m such that prime(m) divides n.
%e A302601 49 is in the sequence because 49 = prime(4)^2 = prime(prime(1)^2)^2.
%e A302601 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset multisystems.
%e A302601 001: {}
%e A302601 003: {{1}}
%e A302601 005: {{2}}
%e A302601 007: {{1,1}}
%e A302601 009: {{1},{1}}
%e A302601 011: {{3}}
%e A302601 017: {{4}}
%e A302601 019: {{1,1,1}}
%e A302601 023: {{2,2}}
%e A302601 025: {{2},{2}}
%e A302601 027: {{1},{1},{1}}
%e A302601 031: {{5}}
%e A302601 041: {{6}}
%e A302601 049: {{1,1},{1,1}}
%e A302601 053: {{1,1,1,1}}
%e A302601 059: {{7}}
%e A302601 067: {{8}}
%e A302601 081: {{1},{1},{1},{1}}
%e A302601 083: {{9}}
%e A302601 097: {{3,3}}
%e A302601 103: {{2,2,2}}
%e A302601 109: {{10}}
%e A302601 121: {{3},{3}}
%e A302601 125: {{2},{2},{2}}
%e A302601 127: {{11}}
%e A302601 131: {{1,1,1,1,1}}
%t A302601 Select[Range[1000],#===1||MatchQ[FactorInteger[#],{{_?(PrimePowerQ[PrimePi[#]]&),_}}]&]
%o A302601 (PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && isprimepower(primepi(p))); \\ _Michel Marcus_, Apr 10 2018
%Y A302601 Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243, A302498.
%K A302601 nonn
%O A302601 1,2
%A A302601 _Gus Wiseman_, Apr 10 2018