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A066767 n-th numerator of Sum_{k=1..inf} d(k)/2^k. 0
1, 5, 14, 35, 76, 164, 336, 687, 1387, 2792, 5596, 11220, 22454, 44932, 89888, 179807, 359632, 719303, 1438626, 2877294, 5754620, 11509276, 23018576, 46037212, 92074455, 184148952, 368297944, 736595944, 1473191918, 2946383908 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are the numerators of the partial sum of Sum_{k=1..inf} d(k)/2^k where d(k) are divisors of k, 1<=d<=k. The denominator of the n-th term is 2^n accordingly. The sequence converges to approximately 2.7440338887594883604802148914922721643114289813196393178485288847379...

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.

LINKS

Table of n, a(n) for n=1..30.

S. R. Finch, Digital Search Tree Constants

EXAMPLE

A(1)=1/2, A(2) = 1/2 + [1+2]/4 since divisors 1=1 and divisors 2 = 1,2, A(3)= 1/2 +[1+2]/4 + [1+3]/8, A(4) = 1/2 + [1+2]/4 + {1+3]/8 + [1+2+4]/16

PROG

(PARI) smv(v)= s=0; for(i=1, matsize(v)[2], s=s+v[i]); s

A066666(n)= sm=0; for(j=1, n, sm=sm+smv(divisors(j)/2^j)); sm

CROSSREFS

Cf. A065442.

Sequence in context: A101015 A076858 A001215 * A227200 A027974 A027983

Adjacent sequences:  A066764 A066765 A066766 * A066768 A066769 A066770

KEYWORD

frac,nonn

AUTHOR

Randall L. Rathbun, Jan 16 2002

STATUS

approved

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Last modified February 20 23:20 EST 2019. Contains 320362 sequences. (Running on oeis4.)