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A137563 Fibonacci numbers with three distinct prime divisors.

%I A137563 #57 Jan 27 2020 08:30:50
%S A137563 610,987,2584,10946,3524578,9227465,24157817,39088169,63245986,
%T A137563 1836311903,7778742049,20365011074,591286729879,4052739537881,
%U A137563 17167680177565,44945570212853,61305790721611591,420196140727489673,1500520536206896083277,6356306993006846248183
%N A137563 Fibonacci numbers with three distinct prime divisors.
%H A137563 Michel Marcus and Amiram Eldar, <a href="/A137563/b137563.txt">Table of n, a(n) for n = 1..83</a> (terms 1..80 from Michel Marcus)
%H A137563 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci Numbers</a>.
%H A137563 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html#100">Prime divisors of Fibonacci numbers</a>.
%F A137563 a(n) = A000045(A114841(n)). - _Michel Marcus_, Mar 24 2018
%e A137563 The distinct prime divisors of the Fibonacci number 610 are 2, 5 and 61.
%e A137563 The distinct prime divisors of the Fibonacci number 44945570212853 are 269, 116849 and 1429913.
%p A137563 with(numtheory): with(combinat): a:=proc(n) if nops(factorset(fibonacci(n)))= 3 then fibonacci(n) else end if end proc: seq(a(n),n=1..110); # _Emeric Deutsch_, May 18 2008
%t A137563 Select[Array[Fibonacci, 120], PrimeNu@ # == 3 &] (* _Michael De Vlieger_, Apr 10 2018 *)
%o A137563 (PARI) lista(nn) = for (n=1, nn, if (omega(f=fibonacci(n))==3, print1(f, ", "))); \\ _Michel Marcus_, Mar 24 2018
%o A137563 (GAP) P1:=List([1..110],n->Fibonacci(n));;
%o A137563 P2:=List([1..Length(P1)],i->Filtered(DivisorsInt(P1[i]),IsPrime));;
%o A137563 a:=List(Filtered([1..Length(P2)],i->Length(P2[i])=3),j->P1[j]); # _Muniru A Asiru_, Mar 25 2018
%Y A137563 Cf. A053409, A114841.
%Y A137563 Intersection of A033992 and A000045. - _Michel Marcus_, Mar 24 2018
%Y A137563 Column k=3 of A303218.
%K A137563 nonn
%O A137563 1,1
%A A137563 _Parthasarathy Nambi_, Apr 25 2008
%E A137563 More terms from _Emeric Deutsch_, May 18 2008