A139590 Fibonacci numbers with a non-Fibonacci number of divisors.

8, 21, 34, 55, 144, 377, 2584, 4181, 6765, 17711, 46368, 75025, 121393, 196418, 317811, 832040, 1346269, 2178309, 5702887, 14930352, 102334155, 165580141, 267914296, 701408733, 1134903170, 4807526976, 12586269025, 32951280099

Offset

1,1

Comments

A000005(a(n)) is a non-Fibonacci number A001690.

Links

Table of n, a(n) for n=1..28.

Example

34 belongs to the sequence because the number of its divisors, 4, is not a Fibonacci number.

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: isA139590 := proc(n) RETURN(isA000045(n) and not isA000045(A000005(n))) ; end: for i from 1 to 130 do a000045 := A000045(i) ; if isA139590(a000045) then printf("%d, ", a000045) ; fi ; od: # R. J. Mathar, May 11 2008
with(combinat): with(numtheory): F:={seq(fibonacci(j), j=1..30)}: a:= proc(n) if member(tau(fibonacci(n)), F) = false then fibonacci(n) else end if end proc: seq(a(n), n=1..50); # Emeric Deutsch

Mathematica

With[{fibs=Fibonacci[Range[60]]}, Transpose[Select[Thread[{fibs, DivisorSigma[ 0, fibs]}], !MemberQ[ fibs, #[[2]]]&]][[1]]] (* Harvey P. Dale, Aug 04 2013 *)

Crossrefs

Cf. A000005, A000045, A001690, A063375, A133021.

Sequence in context: A134862 A302253 A090206 * A154894 A241986 A179681

Adjacent sequences: A139587 A139588 A139589 * A139591 A139592 A139593

Keyword

nonn

Author

Omar E. Pol, May 09 2008

Extensions

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

Status

approved