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%I #25 Sep 08 2022 08:45:02
%S 1,2,2,3,3,4,2,4,4,6,3,7,3,6,6,6,5,7,3,9,4,5,5,9,6,7,6,9,2,11,3,9,6,8,
%T 7,13,6,6,6,12,3,10,5,9,11,8,4,13,5,10,9,11,4,11,7,14,7,6,4,20,4,5,10,
%U 12,9,12,3,11,8,18,2,18,5,10,12,9,6,15,4,17,8,7,8,17,10,7,7,12,4,18,6
%N Number of prime factors of 6^n - 1 (counted with multiplicity).
%H Amiram Eldar, <a href="/A057955/b057955.txt">Table of n, a(n) for n = 1..420</a>
%H S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F Möbius transform of A085031. - _T. D. Noe_, Jun 19 2003
%F a(n) = A001222(A024062(n)). - _Amiram Eldar_, Feb 02 2020
%e 6^10 - 1 = 60466175 = 5^2 * 7 * 11 * 101 * 311 and a(10) = bigomega(60466175) = 2+1+1+1+1 = 6. - _Bernard Schott_, Feb 02 2020
%t PrimeOmega[6^Range[100]-1] (* _Harvey P. Dale_, Dec 14 2015 *)
%o (Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; [f(6^n - 1):n in [1..90]]; // _Marius A. Burtea_, Feb 02 2020
%Y bigomega(b^n-1): A057951 (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), this sequence (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).
%Y Cf. A001222, A024062, A085031, A274907.
%K nonn
%O 1,2
%A _Patrick De Geest_, Nov 15 2000