%I #6 Apr 23 2015 11:04:47
%S 1,1,2,3,5,13,18,31,49,129,178,485,663,1811,4285,6096,10381,26858,
%T 37239,101336,239911,581158,821069,2223296,3044365,8312026,11356391,
%U 31024808,42381199,158168405,200549604,358718009,917985622,2194689253,5307364128
%N Sequence of denominators of the continued fraction derived from the sequence of the numbers of distinct factors of a number (A001221, also called omega(n)).
%C The limits of the continued fraction is Cd= 0.6123687534182316423985073896748729172179677660718454489694806870..., i.e. the number associated to the sequence of number of distinct primes dividing n.
%e b[1]=1;
%e b[2]=d[2]*b[1] = 1*1 =1 (d[2] is the second element of A001221, i.e. the number of distinct primes dividing 2);
%e b[3]=d[3]*b[2]+b[1]= 1*1+1=2.
%p a:=proc(N) # A is numerator of the continued fraction # B is denominator of the continued fraction # d is the sequence of the number of divisors of a number (A001221), d[1] is the first element. A[1]:=d[1]; A[2]:=d[2]*A[1]+1; B[1]:=1; B[2]:=d[2]*B[1]; for n from 2 by 1 to N-1 do A[n+1]:=d[n+1]*A[n]+A[n-1]; B[n+1]:=d[n+1]*B[n]+B[n-1]; od; end:
%Y Cf. A001221, A112595.
%K frac,nonn
%O 1,3
%A _Giorgio Balzarotti_ and _Paolo P. Lava_, Dec 19 2005