A335976 -id:A335976 - cp's OEIS frontend

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, 336, 342, 348, 354, 360, 372, 378, 384, 390, 396, 402, 408, 414, 420, 432, 444, 450, 456, 462, 468, 480, 492, 504, 510, 516, 522, 528, 540, 546, 552, 558, 564, 570, 576, 588, 594, 600, 612, 624, 630, 636

Offset: 1

Altug Alkan, Jan 07 2017

nonn

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
Unless there is an odd term > 3, this sequence as a set is {1, 2, 3} U 6*(Z^+ \ A335976). - Max Alekseyev, Dec 08 2024

			12 is in the sequence because Fibonacci(12) = 144 is in A000010.

Max Alekseyev, Table of n, a(n) for n = 1..665

Cf. A000010, A000045, A114871, A280592, A335976.

select(k -> numtheory:-invphi(combinat:-fibonacci(k))<>[], [1,2,seq(i,i=3..100,3)]); # Robert Israel, Aug 02 2020

isok(k) = istotient(fibonacci(k)); \\ Altug Alkan, Jul 05 2020

a(28)-a(49) from Jinyuan Wang, Jul 08 2020

Terms a(50) onward from Max Alekseyev, Dec 08 2024

cp's OEIS Frontend

A280681 Numbers k such that Fibonacci(k) is a totient.

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