A302596 Powers of prime numbers of prime index.

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

Author

Gus Wiseman, Apr 10 2018

Keywords

• nonn

Comments

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

Examples

			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}}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A001222, A003963, A005117, A006450, A007716, A056239, A076610, A275024, A047968, A281113, A295924, A301760, A302242, A302243.

Programs

Mathematica

Select[Range[400],MatchQ[FactorInteger[#],{{?(#===1||PrimeQ[PrimePi[#]]&),}}]&]

Formula

Sum_{n>=1} 1/a(n) = 1 + Sum_{p in A006450} 1/(p-1). - Amiram Eldar, Sep 19 2022