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

1,1

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.

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A053409, A114841.

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

Column k=3 of A303218.

Sequence in context: A027514 A246881 A263393 * A301561 A204487 A090177

Adjacent sequences: A137560 A137561 A137562 * A137564 A137565 A137566

Keyword

nonn

Author

Parthasarathy Nambi, Apr 25 2008

Extensions

More terms from Emeric Deutsch, May 18 2008

Status

approved