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A302498 Numbers that are a power of a prime number whose prime index is itself a power of a prime number. 3
1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 25, 27, 31, 32, 41, 49, 53, 59, 64, 67, 81, 83, 97, 103, 109, 121, 125, 127, 128, 131, 157, 179, 191, 211, 227, 241, 243, 256, 277, 283, 289, 311, 331, 343, 353, 361, 367, 401, 419, 431, 461, 509, 512, 529, 547, 563 (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

Andrew Howroyd, Table of n, a(n) for n = 1..1000

EXAMPLE

49 is in the sequence because 49 = 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 constant constant-multiset multisystems.

01: {}

02: {{}}

03: {{1}}

04: {{},{}}

05: {{2}}

07: {{1,1}}

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

09: {{1},{1}}

11: {{3}}

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

17: {{4}}

19: {{1,1,1}}

23: {{2,2}}

25: {{2},{2}}

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

31: {{5}}

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

41: {{6}}

49: {{1,1},{1,1}}

53: {{1,1,1,1}}

59: {{7}}

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

MATHEMATICA

Select[Range[100], Or[#===1, PrimePowerQ[#]&&And@@(Or[#===1, PrimePowerQ[#]]&/@PrimePi/@FactorInteger[#][[All, 1]])]&]

PROG

(PARI) ok(n)={my(p); n == 1 || (isprimepower(n, &p) && (p == 2 || isprimepower(primepi(p))))} \\ Andrew Howroyd, Aug 26 2018

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A076610, A275024, A279789, A295920, A301763, A302242, A302243, A302492, A302493, A302496, A302497.

Sequence in context: A184155 A318612 A318690 * A243497 A214577 A280994

Adjacent sequences:  A302495 A302496 A302497 * A302499 A302500 A302501

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified November 17 08:36 EST 2019. Contains 329217 sequences. (Running on oeis4.)