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Source. P. Erdős, Sur l'irrationalité d'une certaine série, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 17, 765--768. The last paragraph of the note on p. 768. Bibliographic details are on the source card.

Statement

Let $g_1<g_2<\cdots$ be the squarefree numbers. The print reads: "J'ai essayé plusieurs fois de démontrer que $\sum_{n\ge1}g_n/2^{g_n}$ est rationnel [sic] où $g_n$ est la suite des nombres sans facteurs carrés." (p. 768). Erdős adds that he may have missed a simple idea but failed completely.

The word "rationnel" stands as printed. The note concerns irrationality throughout, and the intended word is presumably "irrationnel"; the print does not settle this.

No result is proved; the paragraph records an attempted problem.

Bears on

• Problem 259: the sum here is $\sum_n\mu(n)^2\,n/2^n$, the problem's series. The paper records only that Erdős could not settle it, with the apparent misprint noted above.