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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
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
Sequence in context: A044051 A351204 A083132 * A358459 A358377 A242175
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)