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Numbers k such that k and Fibonacci(k) have the same number of prime factors, counted with multiplicity.
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%I #25 Sep 10 2024 08:44:26

%S 1,3,5,7,9,10,11,13,14,17,22,23,26,29,34,43,47,64,83,94,121,131,137,

%T 359,431,433,449,509,569,571

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

%C 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.

%C a(31) > 1422, if it exists. - _Amiram Eldar_, Sep 10 2024

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

%p 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

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

%o (PARI) is(k) = bigomega(k) == bigomega(fibonacci(k)); \\ _Amiram Eldar_, Sep 10 2024

%Y Cf. A000045, A001222, A038575.

%K nonn,more

%O 1,2

%A _Joseph L. Pe_, Nov 03 2002

%E a(24) from _Harvey P. Dale_, May 01 2008

%E Edited by _R. J. Mathar_, Aug 11 2008

%E More terms from _D. S. McNeil_, Dec 23 2010