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.
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