login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n such that n and the n-th Fibonacci number have the same number of distinct prime factors.
0

%I #17 Oct 14 2023 12:50:34

%S 1,3,4,5,7,10,11,12,13,14,17,22,23,26,29,34,43,47,83,94,131,137,359,

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

%N Numbers n such that n and the n-th Fibonacci number have the same number of distinct prime factors.

%e a(7)=10 because 10 and 10th Fibonacci number(i.e. 55) have the same number of prime factors i.e. 2. - _Shyam Sunder Gupta_, Feb 05 2006

%p with(combinat): with(numtheory): a:=proc(n) if nops(factorset(fibonacci(n)))=nops(factorset(n)) then n else fi end: seq(a(n),n=1..150); # _Emeric Deutsch_, Apr 02 2006

%t Insert[Select[Range[1, 50], Length[FactorInteger[ # ]] ==Length[FactorInteger[Fibonacci[ # ]]] &], 2, 2] (* _Stefan Steinerberger_, Mar 20 2006 *)

%t Select[Range[600],PrimeNu[#]==PrimeNu[Fibonacci[#]]&] (* _Harvey P. Dale_, Oct 14 2023 *)

%Y Cf. A001221, A022307.

%K more,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 06 2002

%E More terms from _Sascha Kurz_, Jan 25 2003

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