Erdős Problem #1135
The Collatz conjecture states that for any positive integer n, there exists a natural number m such that the m-th term of the sequence is 1.
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Open problems about iterated arithmetic functions
What happens when an arithmetic function such as φ, σ or a Collatz-type map is applied repeatedly? Orbits are easy to compute; proofs about all starting values are not.
Erdős Problem #409
Erdős Problem #409
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Erdős Problem #410
Let σ_1(n) = σ(n), the sum of divisors function, and σ_k(n) = σ(σ_k-1(n)). Is it true that lim_k → ∞ σ_k(n)^frac 1 k = ∞?
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Erdős Problem #412
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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Erdős Problem #413
Are there infinitely many barriers for ω?
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Erdős Problem #414
Let h_1(n) = h(n) and h_k(n) = h(h_k-1(n)). Is it true, for any m,n, there exist i and j such that h_i(m) = h_j(n)?
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Erdős Problem #906
Does there exists an entire non-zero transcendental function f : ℂ → ℂ such that for any sequence n₀ < n₁ < ..., z | ∃ k, iteratedDeriv (n k) f z = 0 is dense.
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