OFFSET
1,3
COMMENTS
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.
EXAMPLE
b[1]=1;
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);
b[3]=d[3]*b[2]+b[1]= 1*1+1=2.
MAPLE
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:
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Dec 19 2005
STATUS
approved