A371134 Decimal expansion of Sum_{squarefree k>=1} k / 2^k.

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

Offset

1,2

Comments

Erdős (1981) conjectured and Chen and Ruzsa (1999) proved that this constant is irrational.

Links

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

Yong-Gao Chen and Imre Z. Ruzsa, On the irrationality of certain series, Periodica Mathematica Hungarica, Vol. 38, No. 1 (1999), pp. 31-37.

Paul Erdős, Sur l'irrationalité d'une certaine série, C. R. Acad. Sci. Paris, Sér. 1, Vol. 292 (1981), pp. 765-768.

Formula

Equals Sum_{k>=1} A005117(k) / 2^A005117(k).

Equals Sum_{k>=1} k * mu(k)^2 / 2^k.

Example

1.69790781977962506446424089965347807016709423133847...

Mathematica

RealDigits[Sum[n/2^n, {n, Select[Range[1000], SquareFreeQ]}], 10, 120][[1]]

Crossrefs

Cf. A005117, A008683, A333182, A346173, A371135.

Sequence in context: A052119 A021593 A378487 * A344083 A375594 A019696

Adjacent sequences: A371131 A371132 A371133 * A371135 A371136 A371137

Keyword

nonn,cons

Author

Amiram Eldar, Mar 12 2024

Status

approved