Erdős Problem #1061

The problem

How many solutions are there to

$$\sigma(a)+\sigma(b)=\sigma(a+b)$$

with $a+b\leq x$, where $\sigma$ is the sum of divisors function? Is it $\sim cx$ for some constant $c>0$?

Statement quoted from erdosproblems.com/1061, maintained by Thomas Bloom. Original source: [Gu04]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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