%I #6 Apr 23 2015 11:04:37
%S 0,1,1,2,3,8,11,19,30,79,109,297,406,1109,2624,3733,6357,16447,22804,
%T 62055,146914,355883,502797,1361477,1864274,5090025,6954299,18998623,
%U 25952922,96857389,122810311,219667700,562145711,1343959122,3250063955
%N Sequence of numerators of the continued fraction derived from the sequence of the number 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 a[1]=d[1]=0 (d[1] is the first element of A001221, i.e. the number of distinct primes dividing 1).
%e a[2]=d[2]*a[1]+1=0*1+1=1;
%e a[3]=d[3]*a[2]+a[1]=1*1+0=1.
%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, A112596.
%K frac,nonn
%O 1,4
%A _Giorgio Balzarotti_ and _Paolo P. Lava_, Dec 19 2005