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