%I #32 Apr 29 2022 15:33:21

%S 2,3,4,4,4,7,4,6,6,6,4,9,5,6,8,8,4,11,3,9,9,9,3,12,7,8,9,10,7,15,5,13,

%T 8,8,9,14,5,5,8,13,6,17,6,13,12,8,4,15,6,12,10,11,6,16,10,14,8,10,4,

%U 22,9,7,16,17,9,17,5,12,8,14,4,20,5,9,14,8,10,18

%N Number of prime factors of 10^n - 1 (counted with multiplicity).

%H Max Alekseyev, <a href="/A057951/b057951.txt">Table of n, a(n) for n = 1..352</a> (first 322 terms from Ray Chandler)

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit">Factorizations of 11...11 (Repunit)</a>.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/">Main Tables</a> from the Cunningham Project.

%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>

%F Mobius transform of A085035 - _T. D. Noe_, Jun 19 2003

%F a(n) = Omega(10^n -1) = Omega(R_n) + 2 = A046053(n) + 2 {where Omega(n) = A001222(n) and R_n = (10^n - 1)/9 = A002275(n)}. - _Lekraj Beedassy_, Jun 09 2006

%F a(n) = A001222(A002283(n)). - _Ray Chandler_, Apr 22 2017

%t PrimeOmega[10^Range[70]-1] (* _Jayanta Basu_, May 29 2013 *)

%o (PARI) a(n)=bigomega(10^n-1) \\ _Charles R Greathouse IV_, Sep 14 2015

%Y bigomega(b^n-1): this sequence (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

%Y Cf. A001222, A002283, A046053, A085035, A003020, A046107, A005422, A061075, A102380, A095370, A147556, A081317, A081318, A102347, A112505.

%K nonn

%O 1,1

%A _Patrick De Geest_, Nov 15 2000

%E Erroneous b-file replaced by _Ray Chandler_, Apr 26 2017