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A126226 Continued fraction of Product_{primes p} ((p-1)/p)^(1/p). 1

%I #11 Dec 29 2023 11:50:21

%S 0,1,1,3,1,2,11,1,1,4,1,9,2,2,1,1,4,4,2,2,2,1,14,1,2,2,2,7,2,2,1,1,4,

%T 2,4,1,11,7,2,8,32,2,1,293,2,145,1,2,1,21,1,1,3,1,1,8,8,5,2,3,4,3,1,3,

%U 1,1,1,1,3,2,1,3,1,2,2,1,2,19,3,2,1,15,1,2,1,2,5,3,1,1,1,38,1,10,1,2,1,80,1

%N Continued fraction of Product_{primes p} ((p-1)/p)^(1/p).

%C This might be interpreted as the expected value of phi(n)/n for very large n. - _David W. Wilson_, Dec 05 2006

%e 0.55986561693237348...

%o (PARI) contfrac(exp(-suminf(m=2,log(zeta(m))*sumdiv(m,k,if(k<m,moebius(k)/(m-k),0)))))

%Y Cf. A124175, A085548, A085541, A085964, A085965, A085966, A085967, A085968, A085969.

%K cofr,nonn

%O 0,4

%A _Martin Fuller_, Dec 20 2006

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