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A371134
Decimal expansion of Sum_{squarefree k>=1} k / 2^k.
1
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
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
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 12 2024
STATUS
approved