OFFSET
0,1
FORMULA
Prod_{p prime} 1 - (1 - 1/p)*Sum_{q prime} p^-q.
EXAMPLE
0.6504456084219126913904443611046...
MAPLE
eser := 1-x^2+x^4 ;
for pidx from 3 to 100 do
p := ithprime(pidx) ;
eser := eser -x^p+x^(p+1) ;
end do:
eser := taylor(eser, x=0, p) ;
gfun[seriestolist](eser) ;
subsop(1=NULL, %) ;
L := EULERi(%) ;
Digits := 180 ;
x := 1.0 ;
for i from 2 to nops(L) do
if op(i, L) <> 0 then
x := x*evalf(Zeta(i)^op(i, L)) ;
printf("%.70f\n", x) ;
fi ;
end do; # R. J. Mathar, Jul 11 2016
PROG
(PARI) leps=log(2)*(1-bitprecision(1.))
f(x)=my(s=0.); forprime(p=2, 1-leps/log(x), s+=x^-p); s
6/Pi^2*prodeuler(p=2, 1e6, (1-(1-1/p)*f(p))/(1-1/p^2))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Charles R Greathouse IV, Jul 01 2016
STATUS
approved