A114842 - OEIS

%I #21 Oct 14 2019 06:54:07

%S 8,9,10,12,14,19,22,25,26,31,34,41,53,59,61,71,73,79,89,94,101,107,

%T 109,113,121,127,151,167,173,191,193,199,227,251,271,277,293,331,353,

%U 397,401,467,587,599,601,613,631,653,743,991,1091,1223,1373

%N Indices of Fibonacci numbers with 2 distinct prime factors.

%C A072381 is subsequence, since the only square Fibonacci numbers are 1 and 144 which are not squares of primes. - _Charles R Greathouse IV_, Sep 24 2012

%H Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek, <a href="https://doi.org/10.3792/pjaa.81.17">On Fibonacci numbers with few prime divisors</a>, Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 2 (2005), 17-20.

%e a(1) = 8 because 8th Fibonacci number consists of 2 distinct prime factors (i.e. 21 = 3*7).

%e 25 is in the sequence because Fibonacci(25) = 75025 = 5^2 * 3001 consists of 2 distinct prime factors.

%o (PARI) n=1;while(n<355,if(omega(fibonacci(n))==2,print1(n,", "));n++)

%Y Cf. A114823-A114826, A114836-A114841.

%Y Column k=2 of A303217.

%K hard,more,nonn

%O 1,1

%A _Shyam Sunder Gupta_, Feb 19 2006

%E a(40)-a(50) from _Donovan Johnson_, Sep 27 2008

%E a(51)-a(52) from _Max Alekseyev_, Aug 18 2013

%E a(53) from _Amiram Eldar_, Oct 14 2019