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A254061 Decimal expansion of the generalized continued fraction with terms sigma(n)/n for n>=1. 2

%I

%S 4,9,2,2,7,6,7,6,1,3,8,3,0,7,9,9,4,1,1,6,5,9,5,7,1,7,8,6,6,5,9,3,6,4,

%T 2,1,7,8,1,4,2,3,6,1,8,6,9,2,5,6,4,9,6,0,3,2,6,7,7,6,0,2,4,3,4,0,1,4,

%U 2,3,4,1,6,5,8,6,1,2,2,3,9,6,5,6,8,2,6,0,5,3,7,2,4,6,6,8,4,8,3,8,1,3,9,0,4

%N Decimal expansion of the generalized continued fraction with terms sigma(n)/n for n>=1.

%C The values of sigma(n)/n are: 1/1, 3/2, 4/3, 7/4, 6/5, ...

%C This is the limit of the expression 1/(1 + 3/(2 + 4/(3 + 7/(4 + .../...)))).

%e 0.4922767613830799411659571786659364217814236186925...

%o (PARI) value(nn=100) = {my(v = vector(nn, n, sigma(n)/n)); for (n=1, nn, val = v[n]; forstep(k=n-1, 1, -1, val = numerator(v[k])/(denominator(v[k]) + val););); print1(val*1.0);}

%Y Cf. A017665 and A017666 (numerator and denominator of sigma(n)/n).

%Y Cf. A254059, A254060.

%K nonn,cons

%O 0,1

%A _Michel Marcus_, Jan 24 2015

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