A112595 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)).

0, 1, 1, 2, 3, 8, 11, 19, 30, 79, 109, 297, 406, 1109, 2624, 3733, 6357, 16447, 22804, 62055, 146914, 355883, 502797, 1361477, 1864274, 5090025, 6954299, 18998623, 25952922, 96857389, 122810311, 219667700, 562145711, 1343959122, 3250063955

Offset

1,4

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

a[1]=d[1]=0 (d[1] is the first element of A001221, i.e. the number of distinct primes dividing 1).
a[2]=d[2]*a[1]+1=0*1+1=1;
a[3]=d[3]*a[2]+a[1]=1*1+0=1.

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, A112596.

Sequence in context: A138756 A291202 A091076 * A041075 A041893 A206241

Adjacent sequences: A112592 A112593 A112594 * A112596 A112597 A112598

Keyword

frac,nonn

Author

Giorgio Balzarotti and Paolo P. Lava, Dec 19 2005

Status

approved