Problem 468

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Statement. For any $n$ let $D_n$ be the set of sums of the shape $d_1,d_1+d_2,d_1+d_2+d_3,\ldots$ where $1<d_1<d_2<\cdots$ are the divisors of $n$.

What is the size of $D_n\backslash \cup_{m<n}D_m$?

If $f(N)$ is the minimal $n$ such that $N\in D_n$ then is it true that $f(N)=o(N)$? Perhaps just for almost all $N$?

Status. Open.

Source. erdosproblems.com/468, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #468, https://www.erdosproblems.com/468.

Formalization. None recorded.

Progress

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Known Results

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