cp's OEIS Frontend

A302596 Powers of prime numbers of prime index.

%I A302596 #7 Sep 19 2022 07:23:50
%S A302596 1,3,5,9,11,17,25,27,31,41,59,67,81,83,109,121,125,127,157,179,191,
%T A302596 211,241,243,277,283,289,331,353,367,401,431,461,509,547,563,587,599,
%U A302596 617,625,709,729,739,773,797,859,877,919,961,967,991,1031,1063,1087,1153
%N A302596 Powers of prime numbers of prime index.
%C A302596 A prime index of n is a number m such that prime(m) divides n.
%H A302596 Amiram Eldar, <a href="/A302596/b302596.txt">Table of n, a(n) for n = 1..10000</a>
%F A302596 Sum_{n>=1} 1/a(n) = 1 + Sum_{p in A006450} 1/(p-1). - _Amiram Eldar_, Sep 19 2022
%e A302596 Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
%e A302596 001: {}
%e A302596 003: {{1}}
%e A302596 005: {{2}}
%e A302596 009: {{1},{1}}
%e A302596 011: {{3}}
%e A302596 017: {{4}}
%e A302596 025: {{2},{2}}
%e A302596 027: {{1},{1},{1}}
%e A302596 031: {{5}}
%e A302596 041: {{6}}
%e A302596 059: {{7}}
%e A302596 067: {{8}}
%e A302596 081: {{1},{1},{1},{1}}
%e A302596 083: {{9}}
%e A302596 109: {{10}}
%e A302596 121: {{3},{3}}
%e A302596 125: {{2},{2},{2}}
%t A302596 Select[Range[400],MatchQ[FactorInteger[#],{{_?(#===1||PrimeQ[PrimePi[#]]&),_}}]&]
%Y A302596 Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A047968, A281113, A295924, A301760, A302242, A302243.
%K A302596 nonn
%O A302596 1,2
%A A302596 _Gus Wiseman_, Apr 10 2018