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A302596
Powers of prime numbers of prime index.
4
1, 3, 5, 9, 11, 17, 25, 27, 31, 41, 59, 67, 81, 83, 109, 121, 125, 127, 157, 179, 191, 211, 241, 243, 277, 283, 289, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 625, 709, 729, 739, 773, 797, 859, 877, 919, 961, 967, 991, 1031, 1063, 1087, 1153
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = 1 + Sum_{p in A006450} 1/(p-1). - Amiram Eldar, Sep 19 2022
EXAMPLE
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
001: {}
003: {{1}}
005: {{2}}
009: {{1},{1}}
011: {{3}}
017: {{4}}
025: {{2},{2}}
027: {{1},{1},{1}}
031: {{5}}
041: {{6}}
059: {{7}}
067: {{8}}
081: {{1},{1},{1},{1}}
083: {{9}}
109: {{10}}
121: {{3},{3}}
125: {{2},{2},{2}}
MATHEMATICA
Select[Range[400], MatchQ[FactorInteger[#], {{_?(#===1||PrimeQ[PrimePi[#]]&), _}}]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved