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%I #25 Apr 15 2023 13:44:22
%S 1,1,2,1,3,2,3,1,4,2,3,3,4,2,6,2,4,4,4,2,6,3,5,3,7,3,6,3,3,4,5,2,6,4,
%T 7,5,5,4,10,3,5,5,5,4,11,2,4,3,6,6,9,2,4,6,7,5,8,3,7,6,6,4,10,2,10,7,
%U 6,4,8,4,6,7,5,2,14,4,9,5,4,4,10,4,6,8,11,4,8,3,4,8,11,4,9,5,10,4,9,8,12,6
%N Number of prime factors of 4^n + 1 (counted with multiplicity).
%H Max Alekseyev, <a href="/A057940/b057940.txt">Table of n, a(n) for n = 1..561</a> (first 531 terms from Amiram Eldar)
%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%F a(n) = A057957(2n) - A057957(n). - _T. D. Noe_, Jun 19 2003
%F a(n) = Omega(4^n + 1) = A001222(A052539(n)). - _Wesley Ivan Hurt_, Jan 28 2014
%F a(n) = A054992(2*n). - _Amiram Eldar_, Feb 01 2020
%p with(numtheory); A057940:=n->bigomega(4^n + 1); seq(A057940(n), n=1..100); # _Wesley Ivan Hurt_, Jan 28 2014
%t Table[PrimeOmega[4^n + 1], {n, 100}] (* _Wesley Ivan Hurt_, Jan 28 2014 *)
%Y bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), this sequence (b=4), A057941 (b=3), A054992 (b=2).
%Y Cf. A001222, A052539, A057957, A274903.
%K nonn
%O 1,3
%A _Patrick De Geest_, Oct 15 2000
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