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

Author

Omar E. Pol, May 09 2008

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A000005, A000045, A001690, 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: 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 *)

Extensions

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