A137563 - OEIS

%I #57 Jan 27 2020 08:30:50

%S 610,987,2584,10946,3524578,9227465,24157817,39088169,63245986,

%T 1836311903,7778742049,20365011074,591286729879,4052739537881,

%U 17167680177565,44945570212853,61305790721611591,420196140727489673,1500520536206896083277,6356306993006846248183

%N Fibonacci numbers with three distinct prime divisors.

%H 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 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci Numbers</a>.

%H 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 a(n) = A000045(A114841(n)). - _Michel Marcus_, Mar 24 2018

%e The distinct prime divisors of the Fibonacci number 610 are 2, 5 and 61.

%e The distinct prime divisors of the Fibonacci number 44945570212853 are 269, 116849 and 1429913.

%p 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 Select[Array[Fibonacci, 120], PrimeNu@ # == 3 &] (* _Michael De Vlieger_, Apr 10 2018 *)

%o (PARI) lista(nn) = for (n=1, nn, if (omega(f=fibonacci(n))==3, print1(f, ", "))); \\ _Michel Marcus_, Mar 24 2018

%o (GAP) P1:=List([1..110],n->Fibonacci(n));;

%o P2:=List([1..Length(P1)],i->Filtered(DivisorsInt(P1[i]),IsPrime));;

%o a:=List(Filtered([1..Length(P2)],i->Length(P2[i])=3),j->P1[j]); # _Muniru A Asiru_, Mar 25 2018

%Y Cf. A053409, A114841.

%Y Intersection of A033992 and A000045. - _Michel Marcus_, Mar 24 2018

%Y Column k=3 of A303218.

%K nonn

%O 1,1

%A _Parthasarathy Nambi_, Apr 25 2008

%E More terms from _Emeric Deutsch_, May 18 2008