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 A218342 #34 Jan 20 2024 05:01:48
%S A218342 3,4,5,3,7,2,0,6,4,1,0,2,9,8,6,4,8,7,6,7,3,4,9,6,8,2,7,8,9,1,0,3,3,7,
%T A218342 1,0,7,2,0,6,6,5,6,2,5,3,8,0,4,1,5,8,7,2,0,5,6,0,0,4,8,9,6,6,2,5,2,6,
%U A218342 5,3,1,9,5,0,2,2,5,1,8,6,6,9,4,7,9,0,9,1,1,6,1,3,9,2,2,7,6,3,9,6,9,6,4,4,7
%N A218342 Decimal expansion of e^-gamma * Product_(1 - 1/(p^3 - p^2 - p + 1)) where the product is over all primes p.
%C A218342 The average order of Carmichael's lambda function is x/log x * exp(B log log x/log log log x (1 + o(1))), where B is this constant. Under the GRH, the same applies to A036391(n)/n, the sum of the orders mod n of the numbers coprime to n divided by n.
%H A218342 Paul Erdős, Carl Pomerance, and Eric Schmutz, <a href="http://www.math.dartmouth.edu/~carlp/PDF/lambda.pdf">Carmichael's lambda function</a>, Acta Arithmetica 58 (1991), pp. 363-385.
%H A218342 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. 156 (constant C9).
%H A218342 Sungjin Kim, <a href="https://doi.org/10.1142/S1793042116501244">On the order of 'a' modulo 'n' on average</a>, International Journal of Number Theory, Vol. 12, No. 8 (2016), pp. 2073-2080; <a href="https://arxiv.org/abs/1509.03768">arXiv preprint</a>, arXiv:1509.03768 [math.NT], 2015-2016.
%H A218342 Pär Kurlberg and Carl Pomerance, <a href="http://dx.doi.org/10.2140/ant.2013.7.981">On a problem of Arnold: the average multiplicative order of a given integer</a>, Algebra & Number Theory, Vol. 7, No. 4 (2013), pp. 981-999; <a href="http://arxiv.org/abs/1108.5209">arXiv preprint</a>, arXiv:1108.5209 [math.NT], 2012.
%H A218342 R. J. Mathar, <a href="http://arxiv.org/abs/0903.2514">Hardy-Littlewood constants embedded into infinite products over all positive integers</a>, arXiv:0903.2514 [math.NT], 2009-2011; Eq. (106) page 17.
%e A218342 0.34537206410298648767349682789103371072066562538041...
%t A218342 $MaxExtraPrecision = 200; m0 = 1000; dm = 200; digits = 105; Clear[f]; f[m_] := f[m] = (slog = Normal[Series[Log[1 - 1/((p - 1)^2*(p + 1))], {p, Infinity, m}]]; Exp[slog] /. Power[p, n_] -> PrimeZetaP[-n] // N[#, digits + 10] &); f[m = m0]; Print[m, " ", f[m]]; f[m = m + dm]; While[Print[m, " ", f[m]]; RealDigits[f[m], 10, digits + 5] != RealDigits[f[m - dm], 10, digits + 5], m = m + dm]; B = Exp[-EulerGamma]*f[m]; RealDigits[B, 10, digits] // First (* _Jean-François Alcover_, Sep 20 2015 *)
%o A218342 (PARI) exp(-Euler) * prodeulerrat(1-1/((p-1)^2*(p+1))) \\ _Amiram Eldar_, Mar 09 2021
%Y A218342 Cf. A002322, A036391, A080130, A162578.
%K A218342 nonn,cons
%O A218342 0,1
%A A218342 _Charles R Greathouse IV_, Oct 26 2012
%E A218342 More digits from _Jean-François Alcover_, Sep 20 2015