

A286308


Numbers m such that gcd(m, F(m)) = 2, where F(m) denotes the mth 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. 972980, 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



