A064859 Decimal expansion of sum of reciprocals of lcm(1..n) = A003418(n).

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, 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, 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

Offset

1,2

Comments

This constant is irrational (Erdős and Graham, 1980). - Amiram Eldar, Apr 13 2020

Links

Table of n, a(n) for n=1..105.

Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980. See p. 65.

Martin Griffiths and Des MacHale, 99.04 Another irrational number, The Mathematical Gazette, Vol. 99, No. 544 (2015), pp. 130-133.

Michael Penn, An irrational sum, YouTube video, 2022.

Formula

Equals Sum_{j>=1} 1/lcm(1..j).

Example

1.7877804561724665460649343260256627945939617472969608372530269929228902350...

Mathematica

f[n_] := LCM @@ Range@ n; RealDigits[Plus @@ (1/Array[f, 255]), 10, 111][[1]] (* Robert G. Wilson v, Jul 11 2011 *)

Prog

(PARI) suminf(k=1, 1/lcm(vector(k, j, j))) \\ Michel Marcus, Mar 11 2018

Crossrefs

Cf. A003418, A064857, A064858.

Sequence in context: A154192 A011283 A179659 * A364896 A233778 A217168

Adjacent sequences: A064856 A064857 A064858 * A064860 A064861 A064862

Keyword

nonn,cons

Author

Labos Elemer, Oct 08 2001

Status

approved