|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
|
|
LINKS
|
|
|
FORMULA
|
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
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|