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A089189
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Primes p such that p-1 is cube- or higher power-free.
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1
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| The ratio of the count of primes p <= n such that p-1 is cube-free to the count of primes <= n converges to 0.69.. . This implies that roughly 70% of the primes less one are cube-free. This compares to about 0.37 of the primes less one are squarefree.
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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.
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MATHEMATICA
| Select[Prime[Range[100]], Max[Transpose[FactorInteger[#-1]][[2]]]<3&] (* From Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
| Sequence in context: A057447 A095074 A042987 * A097375 A007459 A129944
Adjacent sequences: A089186 A089187 A089188 * A089190 A089191 A089192
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, Feb 05 2012
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