A334072 Decimal expansion of Sum_{k >= 1} 2^(-sigma(k)), where sigma is the sum of divisors function (A000203).

7, 1, 5, 5, 5, 4, 4, 2, 2, 2, 5, 4, 9, 2, 1, 8, 6, 6, 7, 9, 8, 1, 1, 2, 4, 3, 8, 1, 9, 0, 9, 7, 9, 1, 9, 3, 3, 1, 9, 8, 6, 2, 4, 7, 1, 0, 2, 2, 1, 9, 7, 4, 9, 1, 8, 2, 5, 4, 9, 1, 2, 6, 8, 5, 6, 7, 7, 4, 8, 4, 8, 9, 4, 3, 6, 6, 4, 7, 0, 6, 1, 0, 8, 5, 5, 9, 8

Offset: 0

Author

Amiram Eldar, Apr 13 2020

Keywords

• nonn
• cons

Comments

This constant is irrational (Erdős and Graham, 1980).

Examples

			0.71555442225492186679811243819097919331986247102219...
		

Links

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

Crossrefs

Cf. A000203, A334071.

Programs

Mathematica

RealDigits[Sum[2^(-DivisorSigma[1, n]), {n, 1, 2000}], 10, 100][[1]]

PARI

suminf(k=1, 1/2^sigma(k)) \\ Michel Marcus, Apr 14 2020