A137563 Fibonacci numbers with three distinct prime divisors.

610, 987, 2584, 10946, 3524578, 9227465, 24157817, 39088169, 63245986, 1836311903, 7778742049, 20365011074, 591286729879, 4052739537881, 17167680177565, 44945570212853, 61305790721611591, 420196140727489673, 1500520536206896083277, 6356306993006846248183

Offset: 1

Author

Parthasarathy Nambi, Apr 25 2008

Keywords

• nonn

Examples

			The distinct prime divisors of the Fibonacci number 610 are 2, 5 and 61.
The distinct prime divisors of the Fibonacci number 44945570212853 are 269, 116849 and 1429913.
		

Links

• Michel Marcus and Amiram Eldar, Table of n, a(n) for n = 1..83 (terms 1..80 from Michel Marcus)
• Ron Knott, Fibonacci Numbers.
• Ron Knott, Prime divisors of Fibonacci numbers.

Crossrefs

Cf. A053409, A114841.

Intersection of A033992 and A000045. - Michel Marcus, Mar 24 2018

Column k=3 of A303218.

Programs

GAP

P1:=List([1..110],n->Fibonacci(n));;
P2:=List([1..Length(P1)],i->Filtered(DivisorsInt(P1[i]),IsPrime));;
a:=List(Filtered([1..Length(P2)],i->Length(P2[i])=3),j->P1[j]); # Muniru A Asiru, Mar 25 2018

Maple

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

Mathematica

Select[Array[Fibonacci, 120], PrimeNu@ # == 3 &] (* Michael De Vlieger, Apr 10 2018 *)

PARI

lista(nn) = for (n=1, nn, if (omega(f=fibonacci(n))==3, print1(f, ", "))); \\ Michel Marcus, Mar 24 2018

Formula

a(n) = A000045(A114841(n)). - Michel Marcus, Mar 24 2018

Extensions

More terms from Emeric Deutsch, May 18 2008