

A046052


Number of prime factors of Fermat number F(n).


8



1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5
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OFFSET

0,6


COMMENTS

F(12) has 6 known factors with C1133 remaining. [Updated by Walter Nissen, Apr 02 2010]
F(13) has 4 known factors with C2391 remaining.
F(14) has one known factor with C4880 remaining. [Updated by Matt C. Anderson, Feb 14 2010]
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
Factors are counted with multiplicity although it is unknown if all Fermat numbers are squarefree.  Jeppe Stig Nielsen, Jun 09 2018


LINKS

Table of n, a(n) for n=0..11.
W. Keller, Prime factors k.2^n + 1 of Fermat numbers F_m
W. Keller, Summary of factoring status for Fermat numbersF(n)
PSI (The algorithm company), Fermat factor status [Broken link?]
Lorenzo SaurasAltuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).
Eric Weisstein's World of Mathematics, Fermat Number
Wikipedia, Selfridge's Conjecture about Fermat Numbers


FORMULA

a(n) = A001222(A000215(n)).


MATHEMATICA

Array[PrimeOmega[2^(2^#) + 1] &, 9, 0] (* Michael De Vlieger, May 31 2022 *)


PROG

(PARI) a(n)=bigomega(2^(2^n)+1) \\ Eric Chen, Jun 13 2018


CROSSREFS

Cf. A000215, A023394, A229850.
Sequence in context: A168656 A005862 A293254 * A280069 A202276 A029115
Adjacent sequences: A046049 A046050 A046051 * A046053 A046054 A046055


KEYWORD

nonn,more,hard


AUTHOR

Eric W. Weisstein


EXTENSIONS

Name corrected by Arkadiusz Wesolowski, Oct 31 2011


STATUS

approved



