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A302497 Powers of primes of squarefree index. 1
1, 2, 3, 4, 5, 8, 9, 11, 13, 16, 17, 25, 27, 29, 31, 32, 41, 43, 47, 59, 64, 67, 73, 79, 81, 83, 101, 109, 113, 121, 125, 127, 128, 137, 139, 149, 157, 163, 167, 169, 179, 181, 191, 199, 211, 233, 241, 243, 256, 257, 269, 271, 277, 283, 289, 293, 313, 317, 331 (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..59.

EXAMPLE

49 is not in the sequence because 49 = prime(4)^2 but 4 is not squarefree.

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

01: {}

02: {{}}

03: {{1}}

04: {{},{}}

05: {{2}}

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

09: {{1},{1}}

11: {{3}}

13: {{1,2}}

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

17: {{4}}

25: {{2},{2}}

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

29: {{1,3}}

31: {{5}}

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

41: {{6}}

43: {{1,4}}

47: {{2,3}}

59: {{7}}

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

MATHEMATICA

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

PROG

(PARI) is(n) = if(n==1, return(1), my(x=isprimepower(n)); if(x > 0, if(issquarefree(primepi(ceil(n^(1/x)))), return(1)))); 0 \\ Felix Fröhlich, Apr 10 2018

CROSSREFS

Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279788, A281113, A296132, A301768, A302242, A302243, A302478, A302494.

Sequence in context: A266118 A287802 A214207 * A044051 A083132 A302602

Adjacent sequences:  A302494 A302495 A302496 * A302498 A302499 A302500

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 09 2018

STATUS

approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)