A114812 Indices of Fibonacci numbers with 3 prime factors when counted with multiplicity.

6, 15, 16, 21, 25, 33, 35, 37, 38, 39, 46, 49, 51, 58, 62, 65, 67, 82, 86, 103, 106, 119, 122, 139, 142, 145, 158, 166, 179, 181, 226, 233, 235, 241, 257, 263, 274, 281, 299, 301, 317, 337, 383, 389, 419, 457, 463, 473, 479, 491, 521, 541, 557, 619, 643, 659

Offset: 1

Author

Shyam Sunder Gupta, Feb 19 2006

Keywords

• nonn

Comments

1811, 1933, 1997, 2069, 2087, 2203, 2221, 2311, 2663, 2713, 3631, 4157, 4651, 5107, 6701, 7211, 8123 are also terms (from data in Kelly link). - Chai Wah Wu, Nov 11 2019

Examples

			a(2)=15 because 15th Fibonacci number (i.e., 610) consists of 3 prime factors (i.e., 2*5*61).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..83
• Blair Kelly, Fibonacci and Lucas Factorizations.

Crossrefs

Cf. A072381, A114813.

Column k=3 of A303215.

Programs

Mathematica

t = {}; Do[f = FactorInteger[Fibonacci[n]]; If[Total[Transpose[f][[2]]] == 3, AppendTo[t, n]], {n, 2, 100}]; t (* T. D. Noe, Mar 14 2014 *)
Flatten[Position[Fibonacci[Range[700]],?(PrimeOmega[#]==3&)]] (* _Harvey P. Dale, Feb 15 2015 *)

PARI

n=1;while(n<340,if(bigomega(fibonacci(n))==3,print1(n,", "));n++)

Formula

{n: A038575(n)=3}. [R. J. Mathar, Jun 08 2010]

Extensions

More terms from Ryan Propper, May 22 2006