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%I #38 Jan 14 2023 05:19:55
%S 1,7,8,7,7,8,0,4,5,6,1,7,2,4,6,6,5,4,6,0,6,4,9,3,4,3,2,6,0,2,5,6,6,2,
%T 7,9,4,5,9,3,9,6,1,7,4,7,2,9,6,9,6,0,8,3,7,2,5,3,0,2,6,9,9,2,9,2,2,8,
%U 9,0,2,3,5,0,8,2,2,3,2,6,1,5,5,2,8,3,3,6,8,7,8,0,8,5,6,9,7,9,7,9,9,4,6,9,5
%N Decimal expansion of sum of reciprocals of lcm(1..n) = A003418(n).
%C This constant is irrational (Erdős and Graham, 1980). - _Amiram Eldar_, Apr 13 2020
%H Paul Erdős and Ronald L. Graham, <a href="http://www.math.ucsd.edu/~fan/ron/papers/80_11_number_theory.pdf">Old and new problems and results in combinatorial number theory</a>, L'enseignement Mathématique, Université de Genève, 1980. See p. 65.
%H Martin Griffiths and Des MacHale, <a href="https://www.jstor.org/stable/24496914">99.04 Another irrational number</a>, The Mathematical Gazette, Vol. 99, No. 544 (2015), pp. 130-133.
%H Michael Penn, <a href="https://www.youtube.com/watch?v=r6-oqnyUG3g">An irrational sum</a>, YouTube video, 2022.
%F Equals Sum_{j>=1} 1/lcm(1..j).
%e 1.7877804561724665460649343260256627945939617472969608372530269929228902350...
%t f[n_] := LCM @@ Range@ n; RealDigits[Plus @@ (1/Array[f, 255]), 10, 111][[1]] (* _Robert G. Wilson v_, Jul 11 2011 *)
%o (PARI) suminf(k=1, 1/lcm(vector(k, j, j))) \\ _Michel Marcus_, Mar 11 2018
%Y Cf. A003418, A064857, A064858.
%K nonn,cons
%O 1,2
%A _Labos Elemer_, Oct 08 2001
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