cp's OEIS Frontend

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.

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)).

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%I A112596 #6 Apr 23 2015 11:04:47
%S A112596 1,1,2,3,5,13,18,31,49,129,178,485,663,1811,4285,6096,10381,26858,
%T A112596 37239,101336,239911,581158,821069,2223296,3044365,8312026,11356391,
%U A112596 31024808,42381199,158168405,200549604,358718009,917985622,2194689253,5307364128
%N 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)).
%C A112596 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 A112596 b[1]=1;
%e A112596 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);
%e A112596 b[3]=d[3]*b[2]+b[1]= 1*1+1=2.
%p A112596 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 A112596 Cf. A001221, A112595.
%K A112596 frac,nonn
%O A112596 1,3
%A A112596 _Giorgio Balzarotti_ and _Paolo P. Lava_, Dec 19 2005