login
A076212
Numbers k such that k and Fibonacci(k) have the same number of prime factors, counted with multiplicity.
0
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
1,2
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
EXAMPLE
9 is a term because 9 and 9th Fibonacci number (i.e., 34) have the same number of prime factors, i.e., 2.
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[#]] &]
PROG
(PARI) is(k) = bigomega(k) == bigomega(fibonacci(k)); \\ Amiram Eldar, Sep 10 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Joseph L. Pe, Nov 03 2002
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
STATUS
approved