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A066766
Decimal expansion of Sum_{k>=1} sigma(k)/2^k where sigma(k) is the sum of divisors of k, 1 <= d <= k.
9
2, 7, 4, 4, 0, 3, 3, 8, 8, 8, 7, 5, 9, 4, 8, 8, 3, 6, 0, 4, 8, 0, 2, 1, 4, 8, 9, 1, 4, 9, 2, 2, 7, 2, 1, 6, 4, 3, 1, 1, 4, 2, 8, 9, 8, 1, 3, 1, 9, 6, 3, 9, 3, 1, 7, 8, 4, 8, 5, 2, 8, 8, 8, 4, 7, 3, 7, 9, 1, 2, 2, 8, 3, 2, 6, 3, 8, 9, 5, 6, 8, 8, 5, 6, 6, 2, 5, 2, 3, 1, 0, 7, 1, 2, 5, 0, 6, 8, 8, 7, 7, 3, 7, 4, 0
OFFSET
1,1
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]
FORMULA
Equals Sum_{k>=1} k/(2^k - 1). - Amiram Eldar, Jun 22 2020
Faster converging series: Sum_{n >= 1} (1/2)^(n^2) * (n*(4^n - 1) + 2^n)/(2^n - 1)^2. - Peter Bala, Jan 19 2021
From Amiram Eldar, Oct 16 2022: (Start)
Equals Sum_{k>=1} 2^k/(2^k - 1)^2.
Equals A065442 + A065443. (End)
EXAMPLE
2.74403388875948836048021489149227216431142898131963931784...
MAPLE
evalf( add( (1/2)^(n^2) * (n*(4^n - 1) + 2^n)/(2^n - 1)^2, n = 1..20), 100); # Peter Bala, Jan 19 2021
MATHEMATICA
RealDigits[Sum[n/(2^n - 1), {n, 1, 500}], 10, 100][[1]] (* Amiram Eldar, Jun 22 2020 *)
PROG
(PARI) smv(v)= s=0; for(i=1, matsize(v)[2], s=s+v[i]); s
A066766(n)= sm=0; for(j=1, n, sm=sm+smv(divisors(j)/2^j)); sm*1.0
(PARI) suminf(k=1, sigma(k)/2^k) \\ Michel Marcus, Apr 27 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Randall L Rathbun, Jan 16 2002
EXTENSIONS
Name corrected by Paul D. Hanna, Apr 26 2018
STATUS
approved