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 A074738 #38 Aug 30 2023 14:12:22
%S A074738 0,8,6,0,7,1,3,3,2,0,5,5,9,3,4,2,0,6,8,8,7,5,7,3,0,9,8,7,7,6,9,2,2,6,
%T A074738 7,7,7,6,0,5,9,1,1,0,9,5,3,0,3,3,3,1,7,3,4,9,2,0,2,0,2,3,6,6,6,5,4,2,
%U A074738 2,6,3,5,8,1,4,6,2,2,8,7,9,7,9,9,3,8,0,5,3,4,6,0,2,5,2,8,7,6,8,0,7,1,6,3
%N A074738 Decimal expansion of d = 1-(1+log(log(2)))/log(2) = 0.08607133....
%C A074738 An Erdős constant: let s(x) denotes the number of numbers < x expressible as a product of 2 numbers less than or equal to sqrt(x). Erdős showed that S(x) is x/(log x)^(d+o(1)) where d is this constant.
%C A074738 Ford finds that, if H(x,y,z) is the number of integers n <= x which have a divisor in the interval (y,z] and for 3 <= y <= sqrt(x), H(x,y,2y) = x/(((log y)^delta)(log log y)^(3/2)) where delta is the Erdős constant whose decimal digits are A074738. - _Jonathan Vos Post_, Jul 19 2007
%C A074738 Occurs, citing Ford, in p.2 of Koukoulopoulos. - _Jonathan Vos Post_, May 18 2010
%C A074738 Luca & Pomerance call this the Erdős-Tenenbaum-Ford constant and show its relationship to the reduced totient function A002174. - _Charles R Greathouse IV_, Dec 28 2013
%H A074738 G. C. Greubel, <a href="/A074738/b074738.txt">Table of n, a(n) for n = 0..10000</a>
%H A074738 Kevin Ford, <a href="https://arxiv.org/abs/math/0607473">Integers with a divisor in (y,2y]</a>, arXiv:math/0607473 [math.NT], 2006-2013.
%H A074738 Andrew Granville, Cihan Sabuncu, and Alisa Sedunova, <a href="https://arxiv.org/abs/2308.14911">The multiplication table constant and sums of two squares</a>, arXiv:2308.14911 [math.NT], 2023.
%H A074738 Dimitris Koukoulopoulos, <a href="https://arxiv.org/abs/0905.0163">Divisors of shifted primes</a>, arXiv:0905.0163 [math.NT], 2009-2010; International Mathematics Research Notices, 2010:24, pp. 4585-4627.
%H A074738 Florian Luca and Carl Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/rangeoflambda13.pdf">On the range of Carmichael's universal-exponent function</a>, Acta Arithmetica 162 (2014), pp. 289-308.
%H A074738 G. Tenenbaum, <a href="http://www.numdam.org/item?id=CM_1984__51_2_243_0">Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné</a>, Compositio Mathematica, 51 no. 2 (1984), p. 243-263 (see Theorem 1).
%p A074738 evalf(1-(1+log(log(2)))/log(2), 119); # _Alois P. Heinz_, Aug 30 2023
%t A074738 Join[{0}, RealDigits[1 - (1 + Log[Log[2]])/Log[2], 10, 100][[1]]] (* _G. C. Greubel_, Apr 16 2018 *)
%o A074738 (PARI) 1-(1+log(log(2)))/log(2) \\ _Michel Marcus_, Mar 14 2013
%o A074738 (Magma) 1-(1+Log(Log(2)))/Log(2); // _G. C. Greubel_, Apr 16 2018
%K A074738 cons,easy,nonn
%O A074738 0,2
%A A074738 _Benoit Cloitre_, Sep 05 2002