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 A286308 Numbers m such that gcd(m, F(m)) = 2, where F(m) denotes the m-th Fibonacci number. 1
 6, 18, 42, 54, 66, 78, 102, 114, 126, 138, 162, 174, 186, 198, 222, 234, 246, 258, 282, 294, 318, 354, 366, 378, 402, 414, 426, 438, 462, 474, 486, 498, 522, 534, 558, 582, 594, 606, 618, 642, 654, 666, 678, 702, 714, 726, 738, 762, 774, 786, 798, 822, 834, 846, 858 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Amiram Eldar, Aug 07 2020: (Start) All the terms are divisible by 6. Sanna and Tron proved that for all k > 0 (2 in this sequence) the asymptotic density of the sequence of numbers m such that gcd(m, F(m)) = k exists and is equal to Sum_{i>=1} mu(i)/lcm(k*i, A001177(k*i)), where mu is the Möbius function (A008683) and A001177(m) is the least number j such that F(j) is divisible by m. The numbers of terms not exceeding 10^k for k = 1, 2, ... are 1, 6, 62, 625, 6248, 62499, 624900, ... (End) LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Carlo Sanna and Emanuele Tron, The density of numbers n having a prescribed G.C.D. with the nth Fibonacci number Indagationes Mathematicae, Vol. 29, No. 3 (2018), pp. 972-980, preprint, arXiv:1705.01805 [math.NT], 2017. MATHEMATICA Select[Range[1, 1001], GCD[#, Fibonacci[#]]==2 &] (* Indranil Ghosh, May 06 2017 *) PROG (PARI) isok(n) = gcd(n, fibonacci(n)) == 2; (Python) from sympy import fibonacci, gcd [n for n in range(1001) if gcd(n, fibonacci(n)) == 2] # Indranil Ghosh, May 06 2017 CROSSREFS Cf. A000045, A001177, A008683, A074215, A104714. Sequence in context: A191829 A023620 A074837 * A015942 A009945 A270683 Adjacent sequences:  A286305 A286306 A286307 * A286309 A286310 A286311 KEYWORD nonn AUTHOR Michel Marcus, May 05 2017 STATUS approved

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Last modified May 9 23:39 EDT 2021. Contains 343746 sequences. (Running on oeis4.)