Erdős problem 412 · problems.science

Let $σ_1(n)=σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ . Is it true that, for every $m, n ≥ 2$ , there exist some $i, j$ such that $σ_i(m) = σ_j(n)$ ?

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412.lean

Retained formal statement1 of 1

Let $σ_1(n)=σ(n)$ , the sum of divisors function, and $σ_k(n) = σ(σ_{k-1}(n))$ . Is it true that, for every $m, n ≥ 2$ , there exist some $i, j$ such that $σ_i(m) = σ_j(n)$ ?

FormalConjectures/ErdosProblems/412.leanErdos412.erdos_4121 lineExact file

1True ↔ ∀ m ≥ 2, ∀ n ≥ 2, ∃ i j, (⇑(ArithmeticFunction.sigma 1))^[i] m = (⇑(ArithmeticFunction.sigma 1))^[j] n

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