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A302602 Numbers that are powers of a prime number whose prime index is either 1 or also a prime number. 0
1, 2, 3, 4, 5, 8, 9, 11, 16, 17, 25, 27, 31, 32, 41, 59, 64, 67, 81, 83, 109, 121, 125, 127, 128, 157, 179, 191, 211, 241, 243, 256, 277, 283, 289, 331, 353, 367, 401, 431, 461, 509, 512, 547, 563, 587, 599, 617, 625, 709, 729, 739, 773, 797, 859, 877, 919 (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

25 is in the sequence because 25 = prime(3)^2 and 3 is a prime number.

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

01: {}

02: {{}}

03: {{1}}

04: {{},{}}

05: {{2}}

08: {{},{},{}}

09: {{1},{1}}

11: {{3}}

16: {{},{},{},{}}

17: {{4}}

25: {{2},{2}}

27: {{1},{1},{1}}

31: {{5}}

32: {{},{},{},{},{}}

41: {{6}}

59: {{7}}

64: {{},{},{},{},{},{}}

67: {{8}}

81: {{1},{1},{1},{1}}

83: {{9}}

MATHEMATICA

Select[Range[1000], #===1||MatchQ[FactorInteger[#], {{_?(#===2||PrimeQ[PrimePi[#]]&), _}}]&]

PROG

(PARI) isok(n) = (n==1) || ((isprimepower(n, &p)) && ((p==2) || isprime(primepi(p)))); \\ Michel Marcus, Apr 10 2018

CROSSREFS

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

Sequence in context: A302497 A044051 A083132 * A242175 A325662 A275771

Adjacent sequences:  A302599 A302600 A302601 * A302603 A302604 A302605

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 10 2018

STATUS

approved

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Last modified July 15 00:20 EDT 2020. Contains 335762 sequences. (Running on oeis4.)