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%I #2 Jan 09 2009 03:00:00
%S 1,3,9,21,51,105,231,471,975,1965,4011,8031,16221,32475,65205,130485,
%T 261555,523131,1047417,2094957,4191975,8384229,16772835,33545715,
%U 67100115,134200785,268418001,536837061,1073707971,2147415981
%N Number of rationals in [0, 1) consisting just of repeating bits of period at most n.
%F a(n) = sum_{i=1..n} sum_{d|i} (2^d - 1) * mu(i/d)
%e 1/6 = 0.0010101... has repeating bits of period 2, but is not counted because it has a preperiodic part (i.e., the repetition doesn't start immediately after the binary point). Also, 0 = 0.000... is counted and considered to have period 1.
%e a(1) = |{0 = 0.(0)...}| = 1
%e a(2) = |{0 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)...}| = 3
%t Table[Sum[Plus@@((2^Divisors[i]-1)MoebiusMu[i/Divisors[i]]),{i,1,n}],{n,1,30 }]
%Y Partial sums of A038199.
%K nonn,base,easy
%O 1,2
%A Brad Chalfan (brad(AT)chalfan.net), May 29, 2006
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