Erdős problem 1061 · problems.science

For $S(x) = \#\{(a,b) : a + b \le x,\ \sigma(a) + \sigma(b) = \sigma(a+b)\}$ , is $S(x) \sim cx$ ? The preprint claims $S(x)$ grows faster than $x (\log x)^R$ for every fixed $R$ , ruling out the linear asymptotic.

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FormalConjectures/ErdosProblems/

1061.lean

Retained formal statement1 of 1

How many (ordered) solutions are there to σ(a) + σ(b) = σ(a + b) with a + b ≤ x? Is it true that this number is asymptotic to c * x for some constant c > 0?

FormalConjectures/ErdosProblems/1061.leanErdos1061.erdos_10611 lineExact file

1True ↔ ∃ c, 0 < c ∧ Asymptotics.IsEquivalent Filter.atTop Erdos1061.S fun x => c * x

OpenStatement only, no proof

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