A114841 Indices of Fibonacci numbers with 3 distinct prime factors.

15, 16, 18, 21, 33, 35, 37, 38, 39, 46, 49, 51, 58, 62, 65, 67, 82, 86, 103, 106, 119, 122, 125, 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, 706, 719, 739, 751, 857, 863, 877, 881, 883, 911, 947, 983, 1021, 1033, 1061, 1069, 1109, 1117, 1123, 1181, 1187, 1193, 1213, 1226

Offset: 1

Author

Shyam Sunder Gupta, Feb 19 2006

Keywords

• nonn

Examples

			a(1) = 15 because 15th Fibonacci number has 3 distinct prime factors (i.e., 610 = 2 * 5 * 61).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..83
• Blair Kelly, Fibonacci and Lucas Factorizations.
• Prapanpong Pongsriiam, Fibonacci and Lucas Numbers which have Exactly Three Prime Factors and Some Unique Properties of F18 and L18, Fibonacci Quart. 57 (2019), no. 5, 130-144.

Crossrefs

Cf. A114823, A114824, A114825, A114826, A114836, A114837, A114838, A114839, A114840.

Column k=3 of A303217.

Programs

Magma

[n: n in [1..350] |(#(PrimeDivisors(Fibonacci(n)))) eq 3]; // Vincenzo Librandi, Mar 26 2018

Maple

with(numtheory): with(combinat):
a:=n->`if`(nops(factorset(fibonacci(n)))=3,n,NULL); [seq(a(n),n=1..300)]; # Muniru A Asiru, Mar 25 2018

Mathematica

Select[Range[500], PrimeNu[Fibonacci[#]]==3 &] (* Vincenzo Librandi, Mar 26 2018 *)

PARI

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

Extensions

More terms from Ryan Propper, Apr 26 2006

a(57)-a(80) from Max Alekseyev, Aug 18 2013