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A066767 a(n) = Sum_{k=1..n} sigma(k)*2^(n-k) where sigma(k) = A000203(k) is the sum of divisors of 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
a(n) is the numerator of the unreduced fraction of the n-th partial sum of Sum_{k>=1} sigma(k)/2^k where the denominator of that unreduced fraction is 2^n. The partial sums converge to A066766 = 2.744033...
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
LINKS
Steven R. Finch, Digital Search Tree Constants [Broken link]
Steven R. Finch, Digital Search Tree Constants [From the Wayback machine]
EXAMPLE
a(1) = 2*(1/2);
a(2) = 4*(1/2 + (1+2)/4) since sigma(1) = 1 and sigma(2) = 1 + 2 = 3;
a(3) = 8*(1/2 + (1+2)/4 + (1+3)/8);
a(4) = 16*(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
a(n)= sm=0; for(j=1, n, sm=sm+smv(divisors(j)/2^j)); sm*2^n
(PARI) a(n) = 2^n*(sum(k=1, n, sigma(k)/2^k)); \\ Michel Marcus, Apr 25 2022
CROSSREFS
Sequence in context: A076858 A001215 A335651 * A227200 A027974 A027983
KEYWORD
nonn
AUTHOR
Randall L Rathbun, Jan 16 2002
STATUS
approved

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Last modified April 15 11:37 EDT 2024. Contains 371681 sequences. (Running on oeis4.)