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%I #37 May 31 2022 12:54:52
%S 1,1,1,1,1,2,2,2,2,3,4,5
%N Number of prime factors of Fermat number F(n).
%C F(12) has 6 known factors with C1133 remaining. [Updated by _Walter Nissen_, Apr 02 2010]
%C F(13) has 4 known factors with C2391 remaining.
%C F(14) has one known factor with C4880 remaining. [Updated by _Matt C. Anderson_, Feb 14 2010]
%C John Selfridge apparently conjectured that this sequence is not monotonic, so at some point a(n+1) < a(n). Related sequences such as A275377 and A275379 already exhibit such behavior. - _Jeppe Stig Nielsen_, Jun 08 2018
%C Factors are counted with multiplicity although it is unknown if all Fermat numbers are squarefree. - _Jeppe Stig Nielsen_, Jun 09 2018
%H W. Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a>
%H W. Keller, <a href="http://www.prothsearch.com/fermat.html#Summary">Summary of factoring status for Fermat numbersF(n)</a>
%H PSI (The algorithm company), <a href="http://www.perfsci.com/prizes.html">Fermat factor status</a> [Broken link?]
%H Lorenzo Sauras-Altuzarra, <a href="https://doi.org/10.26493/2590-9770.1473.ec5">Some properties of the factors of Fermat numbers</a>, Art Discrete Appl. Math. (2022).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/John_Selfridge#Selfridge's_Conjecture_about_Fermat_Numbers">Selfridge's Conjecture about Fermat Numbers</a>
%F a(n) = A001222(A000215(n)).
%t Array[PrimeOmega[2^(2^#) + 1] &, 9, 0] (* _Michael De Vlieger_, May 31 2022 *)
%o (PARI) a(n)=bigomega(2^(2^n)+1) \\ _Eric Chen_, Jun 13 2018
%Y Cf. A000215, A023394, A229850.
%K nonn,more,hard
%O 0,6
%A _Eric W. Weisstein_
%E Name corrected by _Arkadiusz Wesolowski_, Oct 31 2011