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A046052
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Number of prime factors of Fermat number F(n).
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8
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1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5
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graph;
refs;
listen;
history;
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internal format)
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OFFSET
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0,6
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COMMENTS
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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
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LINKS
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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 Sauras-Altuzarra, 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
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FORMULA
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a(n) = A001222(A000215(n)).
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MATHEMATICA
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Array[PrimeOmega[2^(2^#) + 1] &, 9, 0] (* Michael De Vlieger, May 31 2022 *)
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PROG
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(PARI) a(n)=bigomega(2^(2^n)+1) \\ Eric Chen, Jun 13 2018
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CROSSREFS
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Cf. A000215, A023394, A229850.
Sequence in context: A168656 A005862 A293254 * A280069 A202276 A029115
Adjacent sequences: A046049 A046050 A046051 * A046053 A046054 A046055
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KEYWORD
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nonn,more,hard
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Name corrected by Arkadiusz Wesolowski, Oct 31 2011
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STATUS
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approved
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