%I A119919
%S A119919 1,2,3,4,6,9,8,12,18,21,16,24,36,42,51,32,48,72,84,102,105,64,96,144,
%T A119919 168,204,210,231,128,192,288,336,408,420,462,471,256,384,576,672,816,
%U A119919 840,924,942,975,512,768,1152,1344,1632,1680,1848,1884,1950,1965,1024
%N A119919 Table read by antidiagonals: number of rationals in [0, 1) having at 
               most n preperiodic bits, then at most k periodic bits (read up antidiagonals).
%F A119919 a(n, k) = 2^n * sum_{j=1..k} sum_{d|j} (2^d - 1) * mu(j/d)
%e A119919 The binary expansion of 7/24 = 0.010(01)... has 3 preperiodic bits (to 
               the right of the binary point) followed by 2 periodic (i.e., repeating) 
               bits, while 1/2 = 0.1(0)... has one bit of each type. The preperiodic 
               and periodic parts are both chosen to be as short as possible.
%e A119919 a(2, 2) = |{ 0/1 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)..., 1/2 = 
               0.1(0)..., 1/6 = 0.0(01)..., 5/6 = 0.1(10)..., 1/4 = 0.01(0)..., 
               3/4 = 0.11(0)..., 1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 
               0.10(01)..., 11/12 = 0.11(10)...}| = 12
%e A119919 Table begins:
%e A119919 1 3 9 21
%e A119919 2 6 18 42
%e A119919 4 12 36 84
%e A119919 8 24 72 168
%t A119919 Table[2^n Sum[Plus@@((2^Divisors[j]-1)MoebiusMu[j/Divisors[j]]),{j,1,
               k}],{n,0,10},{ k,1,10}]
%Y A119919 Outer product of 2^n (offset 0) and A119917. Also, partial (double) sums 
               of A119918.
%Y A119919 Sequence in context: A098168 A035312 A056230 this_sequence A036561 A082976 
               A047419
%Y A119919 Adjacent sequences: A119916 A119917 A119918 this_sequence A119920 A119921 
               A119922
%K A119919 nonn,base,easy,tabl
%O A119919 1,2
%A A119919 Brad Chalfan (brad(AT)chalfan.net), May 29, 2006