A139589 Fibonacci numbers with Fibonacci number of divisors.

1, 1, 2, 3, 5, 13, 89, 233, 610, 987, 1597, 10946, 28657, 514229, 3524578, 9227465, 24157817, 39088169, 63245986, 433494437, 1836311903, 2971215073, 7778742049, 20365011074, 591286729879, 4052739537881, 17167680177565, 44945570212853

Offset: 1

Author

Omar E. Pol, May 09 2008

Keywords

• nonn

Comments

A000005(a(n)) is a Fibonacci number.

For the terms shown here (in the Data section) the number of divisors is 1 or 2 or 8. - Emeric Deutsch, May 12 2008

Up to n = 104 the number of divisors is still 1, 2 or 8. - Amiram Eldar, Oct 15 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..104

Crossrefs

Cf. A000005, A000045, A063375, A133021.

Programs

Maple

A000045 := proc(n) option remember ; coeftayl( x/(1-x-x^2),x=0,n) ; end: isA000045 := proc(n) local a; for a from 0 do if A000045(a) > n then RETURN(false) ; elif A000045(a)=n then RETURN(true) ; fi ; od: end: A000005 := proc(n) numtheory[tau](n) ; end: isA139589 := proc(n) RETURN(isA000045(n) and isA000045(A000005(n))) ; end: for i from 1 to 130 do a000045 := A000045(i) ; if isA139589(a000045) then printf("%d,",a000045) ; fi ; od: # R. J. Mathar, May 11 2008
with(combinat): with(numtheory): F:={seq(fibonacci(k),k=1..100)}: a:=proc(n) if member(tau(fibonacci(n)),F)=true then fibonacci(n) else end if end proc: seq(a(n),n=1..70); # Emeric Deutsch, May 12 2008

Mathematica

With[{s = Array[Fibonacci, 80]}, Select[s, ! FreeQ[s, DivisorSigma[0, #]] &]] (* Michael De Vlieger, Oct 15 2019 *)

Extensions

More terms from R. J. Mathar and Emeric Deutsch, May 11 2008