On the k-fold iterate of the sum of divisors function
نویسنده
چکیده
Let γ(n) stand for the product of the prime factors of n. The index of composition λ(n) of an integer n ≥ 2 is defined as λ(n) = log n/ log γ(n) with λ(1) = 1. Given an arbitrary integer k ≥ 0 and letting σk(n) be the k-fold iterate of the sum of divisors function, we show that, given any real number ε > 0, λ(σk(n)) < 1 + ε for almost all positive integers n.
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