Search: id:A124175
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%I A124175
%S A124175 5,5,9,8,6,5,6,1,6,9,3,2,3,7,3,4,8,5,7,2,3,7,6,2,2,4,4,2,2,3,4,1,6,
%T A124175 7,1,7,2,5,7,6,6,6,3,7,0,2,1,2,9,0,6,0,3,9,5,5,4,2,3,3,9,3,3,9,3,5,
%U A124175 2,0,3,1,7,1,7,9,7,5,9,1,5,9,3,6,2,7,6,5,4,0,9,5,0,6,3,0,6,6,5,4,7
%N A124175 Decimal expansion of Prod_{primes p} ((p-1)/p)^(1/p)).
%C A124175 This might be interpreted as the expected value of phi(n)/n for very 
               large n.
%H A124175 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeZetaFunction.html">Prime Zeta Function</a>
%F A124175 exp(-suminf(h=1, primezeta(h+1)/h)) (Robert Gerbicz)
%e A124175 0.5598656169323734857237622442234167172576663702129060395542339339\
%e A124175 352031717975915936276540950630665470795373094197373037280781542375...
%o A124175 (PARI) default(realprecision,256);(f(k)=return(sum(n=1,512,moebius(n)/
               n*log(zeta(k*n)))));exp(sum(h=1,512,-1/h*f(h+1))) /*Robert Gerbicz*/
%o A124175 (PARI) exp(-suminf(m=2,log(zeta(m))*sumdiv(m,k,if(k<m,moebius(k)/(m-k),
               0)))) /*Martin Fuller*/
%Y A124175 Cf. A126226, A085548, A085541, A085964-A085969.
%Y A124175 Sequence in context: A046600 A030798 A021951 this_sequence A163980 A011986 
               A047880
%Y A124175 Adjacent sequences: A124172 A124173 A124174 this_sequence A124176 A124177 
               A124178
%K A124175 nonn,cons
%O A124175 0,1
%A A124175 David W. Wilson, Dec 05 2006
%E A124175 Robert Gerbicz computed this to 130 decimal places.

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