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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 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 FrÃ¶hlich, 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.)