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A057938 Number of prime factors of 6^n + 1 (counted with multiplicity).

%I A057938 #29 Apr 15 2025 22:31:08
%S A057938 1,1,2,1,3,3,4,2,3,3,2,2,4,3,5,3,3,6,3,3,6,4,3,4,4,4,5,5,4,9,2,3,6,3,
%T A057938 11,5,4,3,9,5,4,7,2,3,7,5,2,7,7,6,8,4,5,10,8,6,7,3,2,6,3,2,10,3,8,11,
%U A057938 5,5,6,7,4,5,6,5,10,5,6,11,6,6,8,4,5,8,8,5,11,4,3,16,12,4,5,5,10,4,4,5
%N A057938 Number of prime factors of 6^n + 1 (counted with multiplicity).
%H A057938 Max Alekseyev, <a href="/A057938/b057938.txt">Table of n, a(n) for n = 1..430</a> (first 408 terms from Amiram Eldar)
%H A057938 S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F A057938 a(n) = A057955(2n) - A057955(n). - _T. D. Noe_, Jun 19 2003
%F A057938 a(n) = A001222(A062394(n)). - _Amiram Eldar_, Feb 02 2020
%t A057938 PrimeOmega[6^Range[100]+1] (* _Harvey P. Dale_, Mar 10 2013 *)
%o A057938 (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(6^n + 1):n in [1..100]]; // _Marius A. Burtea_, Feb 02 2020
%Y A057938 bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), this sequence (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).
%Y A057938 Cf. A001222, A057955, A062394, A274904.
%K A057938 nonn
%O A057938 1,3
%A A057938 _Patrick De Geest_, Oct 15 2000