This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112595 #8 Apr 07 2025 14:09:07 %S A112595 0,1,1,2,3,8,11,19,30,79,109,297,406,1109,2624,3733,6357,16447,22804, %T A112595 62055,146914,355883,502797,1361477,1864274,5090025,6954299,18998623, %U A112595 25952922,96857389,122810311,219667700,562145711,1343959122,3250063955 %N 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)). %C A112595 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 A112595 a[1]=d[1]=0 (d[1] is the first element of A001221, i.e. the number of distinct primes dividing 1). %e A112595 a[2]=d[2]*a[1]+1=0*1+1=1; %e A112595 a[3]=d[3]*a[2]+a[1]=1*1+0=1. %p A112595 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 A112595 Cf. A001221, A112596. %K A112595 frac,nonn %O A112595 1,4 %A A112595 _Giorgio Balzarotti_ and _Paolo P. Lava_, Dec 19 2005