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 A089189 Primes p such that p-1 is cubefree. 10
 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 127, 131, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 239, 263, 269, 277, 283, 293, 307, 311, 317, 331, 347, 349, 359, 367, 373, 383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The ratio of the count of primes p <= n such that p-1 is cubefree to the count of primes <= n converges to 0.69.. . This implies that roughly 70% of the primes less one are cubefree. This compares to about 0.37 of the primes less one are squarefree. LINKS Reinhard Zumkeller & Vincenzo Librandi, Table of n, a(n) for n = 1..10000 FORMULA A212793(a(n) - 1) = 1. - Reinhard Zumkeller, May 27 2012 EXAMPLE 43 is included because 43-1 = 2*3*7. 41 is omitted because 41-1 = 2^3*5. 97 is omitted because 96 = 2^5*3 since higher powers are also tested for exclusion. MAPLE filter:= p -> isprime(p) and max(seq(t, t=ifactors(p-1)))<=2: select(filter, [2, seq(2*i+1, i=1..1000)]); # Robert Israel, Sep 11 2014 MATHEMATICA f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>2, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; If[f[p-1]==0, AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 15 2009 *) Select[Prime[Range], Max[Transpose[FactorInteger[#-1]][]]<3&] (* Harvey P. Dale, Feb 05 2012 *) PROG (Haskell) a097375 n = a097375_list !! (n-1) a097375_list = filter ((== 1) . a212793 . (subtract 1)) a000040_list -- Reinhard Zumkeller, May 27 2012 (PARI) lista(nn) = forprime(p=2, nn, f = factor(p-1)[, 2]; if ((#f == 0) || vecmax(f) < 3, print1(p, ", ")); ) \\ Michel Marcus, Sep 11 2014 CROSSREFS Cf. A004709, A039787, A097380, A089194 (subsequence). Sequence in context: A057447 A095074 A042987 * A097375 A007459 A129944 Adjacent sequences:  A089186 A089187 A089188 * A089190 A089191 A089192 KEYWORD easy,nonn AUTHOR Cino Hilliard, Dec 08 2003 and Reinhard Zumkeller, Aug 11 2004 EXTENSIONS Corrected and extended by Harvey P. Dale, Feb 05 2012 STATUS approved

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Last modified October 16 06:24 EDT 2019. Contains 328049 sequences. (Running on oeis4.)