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Statement

Open problem (p. 246, end of §1). The paper closes its introduction with an open problem it attributes to Erdős. Let $\epsilon(y)$ be the natural density of the integers having at least one divisor in the interval $[y,2y)$, and $\epsilon'(y)$ the natural density of those having exactly one. The question, quoted: "A-t-on pour y infini $\epsilon'(y)/\epsilon(y)=o(1)$?"

The paper poses the question and proves nothing about it.

Proof pointer

None; the paper states the problem without a result either way.

Read depth

Claims checked: the problem was read on the page image of p. 246. Nothing here is independently reviewed.

Dependencies

None.

Source. G. Tenenbaum, Sur la probabilité qu'un entier possède un diviseur dans un intervalle donné, Compositio Math. 51 (1984), no. 2, 243--263; the edition read is named on the source card.

Bears on

• Problem 446: the question is the problem's second question, $\delta_1(n)=o(\delta(n))$, posed for the half-open interval $[y,2y)$ where the problem uses $(n,2n)$. The paper leaves it open.