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

Author

Labos Elemer, Oct 08 2001

Keywords

• nonn
• cons

Comments

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

Examples

			1.7877804561724665460649343260256627945939617472969608372530269929228902350...
		

Links

• 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.

Crossrefs

Cf. A003418, A064857, A064858.

Programs

Mathematica

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

PARI

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

Formula

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