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A302601 Numbers that are powers of a prime number whose prime index is also a prime power (not including 1). 0
1, 3, 5, 7, 9, 11, 17, 19, 23, 25, 27, 31, 41, 49, 53, 59, 67, 81, 83, 97, 103, 109, 121, 125, 127, 131, 157, 179, 191, 211, 227, 241, 243, 277, 283, 289, 311, 331, 343, 353, 361, 367, 401, 419, 431, 461, 509, 529, 547, 563, 587, 599, 617, 625, 661, 691, 709 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

49 is in the sequence because 49 = prime(4)^2 = prime(prime(1)^2)^2.

Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset multisystems.

001: {}

003: {{1}}

005: {{2}}

007: {{1,1}}

009: {{1},{1}}

011: {{3}}

017: {{4}}

019: {{1,1,1}}

023: {{2,2}}

025: {{2},{2}}

027: {{1},{1},{1}}

031: {{5}}

041: {{6}}

049: {{1,1},{1,1}}

053: {{1,1,1,1}}

059: {{7}}

067: {{8}}

081: {{1},{1},{1},{1}}

083: {{9}}

097: {{3,3}}

103: {{2,2,2}}

109: {{10}}

121: {{3},{3}}

125: {{2},{2},{2}}

127: {{11}}

131: {{1,1,1,1,1}}

MATHEMATICA

Select[Range[1000], #===1||MatchQ[FactorInteger[#], {{_?(PrimePowerQ[PrimePi[#]]&), _}}]&]

PROG

(PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && isprimepower(primepi(p))); \\ Michel Marcus, Apr 10 2018

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A007425, A007716, A056239, A275024, A281113, A295931, A301764, A302242, A302243, A302498.

Sequence in context: A342949 A322400 A322553 * A064076 A050842 A143447

Adjacent sequences:  A302598 A302599 A302600 * A302602 A302603 A302604

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 10 2018

STATUS

approved

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Last modified June 19 22:51 EDT 2021. Contains 345152 sequences. (Running on oeis4.)