Iterates of the sum of the unitary divisors of an integer

Abstract. Given an integer \(k\ge 0\), let \(\sigma_k^*(n)\) stand for the \(k\)-fold iterate of \(\sigma^*(n)\), the sum of the unitary divisors of \(n\). We show that \(\frac{\sigma_2^*(p+1)}{\sigma_1^*(p+1)}\) tends to 1 for almost all primes \(p\).