%I A046051
%S A046051 0,1,1,2,1,3,1,3,2,3,2,5,1,3,3,4,1,6,1,6,4,4,2,7,3,3,3,6,3,7,1,5,4,3,4,
%T A046051 10,2,3,4,8,2,8,3,7,6,4,3,10,2,7,5,7,3,9,6,8,4,6,2,13,1,3,7,7,3,9,2,7,
%U A046051 4,9,3,14,3,5,7,7,4,8,3,10,6,5,2,14,3,5,6,10,1,13,5,9,3,6,5,13,2,5,8
%N A046051 Number of prime factors of Mersenne number M(n) = 2^n - 1 (counted with 
               multiplicity).
%C A046051 Length of row n of A001265.
%H A046051 T. D. Noe, <a href="b046051.txt">Table of n, a(n) for n=1..500</a> (derived 
               from Brillhart et al.)
%H A046051 S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/
               cun/index.html">The Cunningham Project</a>
%H A046051 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MersenneNumber.html">Mersenne Number</a>
%F A046051 Mobius transform of A085021 - T. D. Noe (noe(AT)sspectra.com), Jun 19 
               2003
%e A046051 a(4) = 2 because 2^4 - 1 = 15 = 3*5.
%p A046051 with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(stirling2(n,
               2)) fi end: seq(a(n), n=2..100); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 11 2008
%t A046051 a[q_] := Module[{x, n}, x=FactorInteger[2^n-1]; n=Length[x]; Sum[Table[x[i]][2]], 
               {i, n}][j]], {j, n}]]
%Y A046051 Cf. A000043, A000668, A001348, A054988, A054989, A054990, A054991, A054992, 
               A057951-A057958.
%Y A046051 Cf. A085021.
%Y A046051 Sequence in context: A036459 A079167 A032741 this_sequence A025812 A109698 
               A029231
%Y A046051 Adjacent sequences: A046048 A046049 A046050 this_sequence A046052 A046053 
               A046054
%K A046051 nonn
%O A046051 1,4
%A A046051 Eric Weisstein (eric(AT)weisstein.com).