OFFSET
0,2
COMMENTS
For any multiplicative function g with values -1<= g(k) <= 1, for any real x >=2, Sum( i<= x, g(i) ) << x * exp{ -K * Sum( p<=x, (1-g(p))/p ) } and K is the optimal constant satisfying this inequality ( Hall and Tenenbaum, 1991).
REFERENCES
G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, p. 348, Publications de l'Institut Cartan, 1990.
FORMULA
K = cos(S) = 0.3287... where S it the root 0< S < 2Pi of sin(S)+(Pi-S)*cos(S) = Pi/2.
PROG
(PARI) \p200;
contfrac(cos(solve(X=0, 2*Pi, sin(X)+(Pi-X)*cos(X)-Pi/2)))
CROSSREFS
KEYWORD
base,cofr,easy,nonn
AUTHOR
Benoit Cloitre, Jun 19 2002
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 06 2024
STATUS
approved