A095224 Least squarefree Fibonacci number with exactly n prime divisors.

1, 2, 21, 610, 6765, 701408733, 102334155, 190392490709135, 251728825683549488150424261, 23416728348467685, 13598018856492162040239554477268290, 81055900096023504197206408605

Offset: 0

Author

Amarnath Murthy, Jun 10 2004

Keywords

• nonn

Comments

Conjecture: The sequence is infinite.

Based on a table of the first 300 Fibonacci numbers, factorized.

Number of prime divisors counted with multiplicity. - Harvey P. Dale, Mar 06 2024

Examples

			a(5) = 701408733 = 3 * 43 * 89 * 199 * 307.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..24

Crossrefs

Cf. A022307, A038575. - R. J. Mathar, Oct 14 2010

Programs

Maple

From R. J. Mathar, Oct 14 2010: (Start)
A001221 := proc(n) nops(numtheory[factorset](n)) ; end proc:
A095224 := proc(n) for i from 1 do f := combinat[fibonacci](i) ; if A001221(f) =n and numtheory[bigomega](f) = n then return f ; fi; od ; end proc:
for n from 1 do printf("%d,\n",A095224(n)) ; end do: (End)

Mathematica

Table[SelectFirst[{#,PrimeOmega[#]}&/@Select[Fibonacci[Range[200]],SquareFreeQ],#[[2]] == n&],{n,0,11}][[;;,1]] (* Harvey P. Dale, Mar 06 2024 *)

Formula

min{A000045(i): A038575(i) = A022307(i) = n}. a(n) >= A060319(n). - R. J. Mathar, Oct 14 2010

Extensions

a(9) corrected and 3 terms added by R. J. Mathar, Oct 14 2010