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A280681
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Numbers k such that Fibonacci(k) is a totient.
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2
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1, 2, 3, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72, 84, 90, 96, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 180, 192, 198, 204, 210, 216, 222, 228, 234, 240, 252, 264, 270, 276, 288, 294, 300, 306, 312, 324, 330
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OFFSET
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1,2
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COMMENTS
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Respectively, corresponding Fibonacci numbers are 1, 1, 2, 8, 144, 2584, 46368, 832040, 14930352, 267914296, 4807526976, 86267571272, 1548008755920, 498454011879264, 160500643816367088, 2880067194370816120, ...
Note that sequence does not contain all the positive multiples of 6, e.g., 66 and 102. See A335976 for a related sequence.
Conjecture: Sequence is infinite. - Altug Alkan, Jul 05 2020
All terms > 2 are multiples of 3, because Fibonacci(k) is odd unless k is a multiple of 3. Are all terms > 3 multiples of 6? If a term k is not a multiple of 6, then since Fibonacci(k) is not divisible by 4, Fibonacci(k)+1 must be in A114871. - Robert Israel, Aug 02 2020
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LINKS
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EXAMPLE
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12 is in the sequence because Fibonacci(12) = 144 is in A000010.
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MAPLE
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select(k -> numtheory:-invphi(combinat:-fibonacci(k))<>[], [1, 2, seq(i, i=3..100, 3)]); # Robert Israel, Aug 02 2020
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PROG
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(PARI) isok(k) = istotient(fibonacci(k)); \\ Altug Alkan, Jul 05 2020
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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