This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A124175 #30 Feb 16 2025 08:33:03
%S A124175 5,5,9,8,6,5,6,1,6,9,3,2,3,7,3,4,8,5,7,2,3,7,6,2,2,4,4,2,2,3,4,1,6,7,
%T A124175 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,
%U A124175 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 Product_{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 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 164.
%H A124175 Mathoverflow, <a href="http://mathoverflow.net/questions/230318/asymptotics-of-product-of-eulers-totient-function-a001088">Asymptotics of product of Euler's totient function</a>, 2016.
%H A124175 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>
%F A124175 exp(-suminf(h=1, primezeta(h+1)/h)). - _Robert Gerbicz_
%F A124175 [Notation not clear. Is this perhaps exp(-Sum_{h=1..oo} primezeta(h+1)/h) ? - _N. J. A. Sloane_, Oct 08 2017]
%F A124175 Equals exp(1) * lim_{n->infinity} (A001088(n)/n!)^(1/n). - _Vaclav Kotesovec_, Feb 05 2016
%e A124175 0.5598656169323734857237622442234167172576663702129060395542339339\
%e A124175 352031717975915936276540950630665470795373094197373037280781542375...
%t A124175 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_ *)
%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, A242624, A272028.
%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.