Erdős problem 1061

Let $S(x)$ count ordered pairs $(a,b)$ with $a+b \le x$ and $\sigma(a)+\sigma(b) = \sigma(a+b)$ . Erdos asked whether $S(x) \sim cx$ . The opposite extreme holds: for every $R > 0$ , $S(x)/(x(\log x)^R) \to \infty$ , so the count beats every fixed logarithmic scale.

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

FormalConjectures/ErdosProblems/1061.lean

Formal Conjectures

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

Reported by these sources. Not reviewed here.