This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A046052 #38 Feb 16 2025 08:32:38 %S A046052 1,1,1,1,1,2,2,2,2,3,4,5 %N A046052 Number of prime factors of Fermat number F(n). %C A046052 F(12) has 6 known factors with C1133 remaining. [Updated by _Walter Nissen_, Apr 02 2010] %C A046052 F(13) has 4 known factors with C2391 remaining. %C A046052 F(14) has one known factor with C4880 remaining. [Updated by _Matt C. Anderson_, Feb 14 2010] %C A046052 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 A046052 Factors are counted with multiplicity although it is unknown if all Fermat numbers are squarefree. - _Jeppe Stig Nielsen_, Jun 09 2018 %H A046052 W. Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a> %H A046052 W. Keller, <a href="http://www.prothsearch.com/fermat.html#Summary">Summary of factoring status for Fermat numbersF(n)</a> %H A046052 PSI (The algorithm company), <a href="http://www.perfsci.com/prizes.html">Fermat factor status</a> [Broken link?] %H A046052 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 A046052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a> %H A046052 Wikipedia, <a href="https://en.wikipedia.org/wiki/John_Selfridge#Selfridge's_Conjecture_about_Fermat_Numbers">Selfridge's Conjecture about Fermat Numbers</a> %F A046052 a(n) = A001222(A000215(n)). %t A046052 Array[PrimeOmega[2^(2^#) + 1] &, 9, 0] (* _Michael De Vlieger_, May 31 2022 *) %o A046052 (PARI) a(n)=bigomega(2^(2^n)+1) \\ _Eric Chen_, Jun 13 2018 %Y A046052 Cf. A000215, A023394, A229850. %K A046052 nonn,more,hard %O A046052 0,6 %A A046052 _Eric W. Weisstein_ %E A046052 Name corrected by _Arkadiusz Wesolowski_, Oct 31 2011