A037917 Numbers n such that the Fibonacci number F(n) is divisible by a square.

6, 12, 18, 24, 25, 30, 36, 42, 48, 50, 54, 56, 60, 66, 72, 75, 78, 84, 90, 91, 96, 100, 102, 108, 110, 112, 114, 120, 125, 126, 132, 138, 144, 150, 153, 156, 162, 168, 174, 175, 180, 182, 186, 192, 198, 200, 204, 210, 216, 220, 222, 224, 225, 228, 234, 240

Offset: 1

Author

Marc LeBrun

Keywords

• nonn

Comments

Is a(n) asymptotic to C*n with 4 < C < 4.5 ? - Benoit Cloitre, Sep 04 2002

Numbers are a superset of the multiples of 6 (A008588), because 8 divides Fibonacci(6m) = A134492(m). Sequence apparently also contains the multiples of 25. Are all a(n) composite? Members not divisible by 6 or 25 are 56, 91, 110, 112, 153, 182, 220, 224, 273, 280, ... - Ralf Stephan, Jan 26 2014

These numbers are the positive multiples of A065069. - Charles R Greathouse IV, Feb 02 2014

To address Cloitre's question, if such C exists it must be less than 4.3 using the known terms of A065069. - Charles R Greathouse IV, Feb 04 2014

Links

• Amiram Eldar, Table of n, a(n) for n = 1..328 (terms 1..235 from T. D. Noe, based on Kelly's table)
• Blair Kelly, Fibonacci Factorizations
• Eric Weisstein's World of Mathematics, Fibonacci Number.

Crossrefs

Cf. A000045, A037918, A001177, A030426.

Programs

Mathematica

Select[Range[100], MoebiusMu[Fibonacci[#]] == 0 &] (* Alonso del Arte, Jan 26 2014 *)

PARI

is(n)=!issquarefree(fibonacci(n)) \\ Charles R Greathouse IV, Feb 02 2014

Extensions

More terms from Eric W. Weisstein