A112596 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)).

1, 1, 2, 3, 5, 13, 18, 31, 49, 129, 178, 485, 663, 1811, 4285, 6096, 10381, 26858, 37239, 101336, 239911, 581158, 821069, 2223296, 3044365, 8312026, 11356391, 31024808, 42381199, 158168405, 200549604, 358718009, 917985622, 2194689253, 5307364128

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.

Links

Table of n, a(n) for n=1..35.

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

Cf. A001221, A112595.

Sequence in context: A087356 A281598 A042261 * A179238 A041385 A108282

Adjacent sequences: A112593 A112594 A112595 * A112597 A112598 A112599

Keyword

frac,nonn

Author

Giorgio Balzarotti and Paolo P. Lava, Dec 19 2005

Status

approved