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A057936 Number of prime factors of 8^n + 1 (counted with multiplicity).

%I A057936 #35 Feb 25 2023 17:02:42
%S A057936 2,2,4,2,4,4,4,3,6,6,5,4,4,6,7,3,6,6,5,4,7,6,5,5,7,10,10,5,5,11,5,3,9,
%T A057936 9,11,6,7,8,7,6,7,10,6,7,12,8,7,7,7,14,11,5,6,10,12,8,9,8,8,8,4,9,13,
%U A057936 4,11,12,8,9,8,15,8,8,6,10,12,8,12,17,6,7,15,10,9,12,12,10,11,8,8,18,12
%N A057936 Number of prime factors of 8^n + 1 (counted with multiplicity).
%H A057936 Max Alekseyev, <a href="/A057936/b057936.txt">Table of n, a(n) for n = 1..502</a> (first 354 terms from Amiram Eldar)
%H A057936 S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F A057936 a(n) = A057953(2n) - A057953(n). - _T. D. Noe_, Jun 19 2003
%F A057936 a(n) = A001222(A062395(n)) = A054992(3*n). - _Amiram Eldar_, Feb 02 2020
%t A057936 PrimeOmega[8^Range[100]+1] (* _Harvey P. Dale_, Dec 16 2014 *)
%o A057936 (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(8^n + 1):n in [1..110]]; // _Marius A. Burtea_, Feb 02 2020
%Y A057936 bigomega(b^n+1): A057934 (b=10), A057935 (b=9), this sequence (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).
%Y A057936 Cf. A001222, A057953, A062395, A274905.
%K A057936 nonn
%O A057936 1,1
%A A057936 _Patrick De Geest_, Oct 15 2000