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

1,2

Comments

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

Links

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

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[#]]&), _}}]&]

Crossrefs

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

Sequence in context: A145819 A317827 A296768 * A230721 A094509 A120811

Adjacent sequences: A302593 A302594 A302595 * A302597 A302598 A302599

Keyword

nonn

Author

Gus Wiseman, Apr 10 2018

Status

approved