A333182 Decimal expansion of Sum_{k>=1} mu(k)^2 / 2^k.

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

Offset: 0

Author

Ilya Gutkovskiy, Mar 10 2020

Keywords

• nonn
• cons

Comments

Squarefree constant: binary expansion is the characteristic function of squarefree numbers (A008966).

Examples

			0.93137635638313358... = (0.1110111001...)_2.
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Crossrefs

Cf. A005117, A008683, A008966, A051006, A332905.

Programs

Mathematica

RealDigits[Sum[MoebiusMu[n]^2/2^n, {n, 1, 500}], 10, 100][[1]] (* Amiram Eldar, Jun 22 2020 *)

Formula

Equals Sum_{k>=1} mu(k)/(2^(k^2) - 1). - Amiram Eldar, Jun 22 2020