A076212 Numbers k such that k and Fibonacci(k) have the same number of prime factors, counted with multiplicity.

1, 3, 5, 7, 9, 10, 11, 13, 14, 17, 22, 23, 26, 29, 34, 43, 47, 64, 83, 94, 121, 131, 137, 359, 431, 433, 449, 509, 569, 571

Offset: 1

Author

Joseph L. Pe, Nov 03 2002

Keywords

• nonn
• more

Comments

More precisely, numbers n such that Omega(n) = Omega(Fibonacci(n)), where Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity.

a(31) > 1422, if it exists. - Amiram Eldar, Sep 10 2024

Examples

			9 is a term because 9 and 9th Fibonacci number (i.e., 34) have the same number of prime factors, i.e., 2.
		

Crossrefs

Cf. A000045, A001222, A038575.

Programs

Maple

with(numtheory): with(combinat): a:=proc(n) if bigomega(n)=bigomega(fibonacci(n)) then n else fi end: seq(a(n),n=1..150); # Emeric Deutsch, Feb 15 2006

Mathematica

Select[Range[150], PrimeOmega[#] == PrimeOmega[Fibonacci[#]] &]

PARI

is(k) = bigomega(k) == bigomega(fibonacci(k)); \\ Amiram Eldar, Sep 10 2024

Extensions

a(24) from Harvey P. Dale, May 01 2008

Edited by R. J. Mathar, Aug 11 2008

More terms from D. S. McNeil, Dec 23 2010