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 A254059 a(n) is the numerator of the generalized continued fraction with terms sigma(m)/m for m=1 to n. 2

%I

%S 1,2,10,18,110,146,1902,17406,18138,1063554,1067358,613398,32007426,

%T 3207106806,19364306334,11692834638,7305794123622,49155004502022,

%U 1080060968010858,11832864774651042,21773239326463026,475223541375418782,83304240831298888014

%N a(n) is the numerator of the generalized continued fraction with terms sigma(m)/m for m=1 to n.

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

%e For n=1, the continued fraction is 1/1 so a(1)=1.

%e For n=2, it is 1/(1+3/2) = 2/5, so a(2)=2.

%e For n=3, it is 1/(1+3/(2+4/3)) = 10/19, so a(3)=10.

%o (PARI) a(nn) = {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(numerator(val), ", "););}

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

%Y Cf. A254060 (denominators), A254061.

%K nonn,frac

%O 1,2

%A _Michel Marcus_, Jan 24 2015

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Last modified February 4 12:59 EST 2023. Contains 360055 sequences. (Running on oeis4.)