A346173 -id:A346173 - cp's OEIS frontend

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

Amiram Eldar, Mar 12 2024

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

			1.69790781977962506446424089965347807016709423133847...

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.

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

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

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

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

A371135 Decimal expansion of Sum_{powerful k>=1} k / 2^k.

Original entry on oeis.org

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

Offset: 0

Amiram Eldar, Mar 12 2024

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

			0.79907321982327239944106432321005064531722246539852...

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

Cf. A001694, A112526, A346173, A371134.

RealDigits[Sum[n/2^n, {n, Select[Range[1000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]}], 10, 120][[1]]

Equals Sum_{k>=1} A001694(k) / 2^A001694(k).

Equals Sum_{k>=1} k * A112526(k) / 2^k.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula