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 A124175 Decimal expansion of Product_{primes p} ((p-1)/p)^(1/p)). 12
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This might be interpreted as the expected value of phi(n)/n for very large n. LINKS Mathoverflow, Asymptotics of product of Euler's totient function, 2016. Eric Weisstein's World of Mathematics, Prime Zeta Function FORMULA exp(-suminf(h=1, primezeta(h+1)/h)). - Robert Gerbicz {Notation not clear. Is this perhaps exp(-Sum_{h=1..oo} primezeta(h+1)/h) ? - N. J. A. Sloane, Oct 08 2017) Equals lim_{n->infinity} (A001088(n)/n!)^(1/n). - Vaclav Kotesovec, Feb 05 2016 EXAMPLE 0.5598656169323734857237622442234167172576663702129060395542339339\ 352031717975915936276540950630665470795373094197373037280781542375... MATHEMATICA digits = 100; s = Exp[-NSum[PrimeZetaP[h+1]/h, {h, 1, Infinity}, WorkingPrecision -> digits+5, NSumTerms -> 3 digits]]; RealDigits[s, 10, digits][[1]] (* Jean-François Alcover, Dec 07 2015, after Robert Gerbicz *) PROG (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 */ (PARI) exp(-suminf(m=2, log(zeta(m))*sumdiv(m, k, if(k

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)