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A175130
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Indices of Fibonacci numbers that are not cubefree.
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1
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6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 125, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 250, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324
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OFFSET
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1,1
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COMMENTS
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Conjecture: all terms are multiples of 6 or 125. - _Harvey P. Dale_, Apr 28 2020
The conjecture is false. The counterexamples are 392, 784, 1183, 1210, .... . - _Amiram Eldar_, Oct 16 2023
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LINKS
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FORMULA
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A010056(a(n)) * (1 - A212793(a(n))) = 1. - _Reinhard Zumkeller_, May 27 2012
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EXAMPLE
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Fibonacci(125) = 5^3 * 3001 * 158414167964045700001 = A000045(125) is not cubefree, which adds 125 to the sequence.
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MATHEMATICA
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Select[Range[350], Max[FactorInteger[Fibonacci[#]][[All, 2]]]>2&] (* _Harvey P. Dale_, Apr 28 2020 *)
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PROG
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(Haskell)
import Data.List (findIndices)
a175130 n = a175130_list !! (n-1)
a175130_list = map (+ 1) $ findIndices ((== 0) . a212793) $ tail a000045_list
-- _Reinhard Zumkeller_, May 27 2012
(PARI) is(n)=n>5 && vecmax(factor(fibonacci(n))[, 2])>2 \\ _Charles R Greathouse IV_, Nov 07 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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_R. J. Mathar_, Feb 16 2010
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STATUS
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approved
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