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A057955 Number of prime factors of 6^n - 1 (counted with multiplicity).

%I A057955 #29 Apr 15 2025 22:18:17
%S A057955 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 A057955 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 A057955 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 A057955 Number of prime factors of 6^n - 1 (counted with multiplicity).
%H A057955 Max Alekseyev, <a href="/A057955/b057955.txt">Table of n, a(n) for n = 1..430</a> (terms 1..420 from Amiram Eldar)
%H A057955 S. S. Wagstaff, Jr., <a href="https://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>
%F A057955 Möbius transform of A085031. - _T. D. Noe_, Jun 19 2003
%F A057955 a(n) = A001222(A024062(n)). - _Amiram Eldar_, Feb 02 2020
%e A057955 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 A057955 PrimeOmega[6^Range[100]-1] (* _Harvey P. Dale_, Dec 14 2015 *)
%o A057955 (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 A057955 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 A057955 Cf. A001222, A024062, A085031, A274907.
%K A057955 nonn
%O A057955 1,2
%A A057955 _Patrick De Geest_, Nov 15 2000