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Problem #1061: How many solutions are there...

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 $\sim cx$...

Problem Statement

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 $c>0$?
Categories: Number Theory

Progress

A question of Erdős reported in problem B15 of Guy's collection [Gu04].

Source: erdosproblems.com/1061 | Last verified: January 19, 2026

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