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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
1, 2, 10, 18, 110, 146, 1902, 17406, 18138, 1063554, 1067358, 613398, 32007426, 3207106806, 19364306334, 11692834638, 7305794123622, 49155004502022, 1080060968010858, 11832864774651042, 21773239326463026, 475223541375418782, 83304240831298888014 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

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

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

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

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

PROG

(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), ", "); ); }

CROSSREFS

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

Cf. A254060 (denominators), A254061.

Sequence in context: A134251 A317714 A055260 * A346551 A180591 A330083

Adjacent sequences: A254056 A254057 A254058 * A254060 A254061 A254062

KEYWORD

nonn,frac

AUTHOR

Michel Marcus, Jan 24 2015

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)