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A057935 Number of prime factors of 9^n + 1 (counted with multiplicity).

%I A057935 #23 Sep 08 2022 08:45:02
%S A057935 2,2,3,3,4,3,4,2,4,3,4,6,4,4,6,2,4,4,4,5,7,5,4,4,8,4,5,6,4,7,5,2,6,5,
%T A057935 9,8,5,6,7,5,5,10,7,6,9,4,4,6,9,6,8,7,6,9,8,9,9,5,3,11,6,4,11,6,8,9,9,
%U A057935 8,6,9,5,6,6,6,13,4,8,7,5,4,7,6,5,11,8,5,8,7,4,11,7,9,9,5,9,7,5,6,10,7,6
%N A057935 Number of prime factors of 9^n + 1 (counted with multiplicity).
%H A057935 Max Alekseyev, <a href="/A057935/b057935.txt">Table of n, a(n) for n = 1..345</a> (first 329 terms from Amiram Eldar)
%H A057935 S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F A057935 a(n) = A057952(2n) - A057952(n). - _T. D. Noe_, Jun 19 2003
%F A057935 a(n) = A001222(A062396(n)) = A057941(2*n). - _Amiram Eldar_, Feb 02 2020
%t A057935 PrimeOmega[Table[9^n + 1, {n, 1, 30}]] (* _Amiram Eldar_, Feb 02 2020 *)
%o A057935 (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(9^n + 1):n in [1..100]]; // _Marius A. Burtea_, Feb 02 2020
%Y A057935 bigomega(b^n+1): A057934 (b=10), this sequence  (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).
%Y A057935 Cf. A002592, A046053, A001222, A057941, A057952, A062396.
%K A057935 nonn
%O A057935 1,1
%A A057935 _Patrick De Geest_, Oct 15 2000