We define ψ‾ to be the multiplicative arithmetic function that satisfies
for all primes
p and positive integers α. Let
λ(n) be the number of iterations of the function
ψ‾ needed for
n to reach 2. It follows from a theorem due to White that
λ is additive. Following Shapiro's work on the iterated
φ function, we determine bounds for
λ. We also use the function
λ to partition the set of positive integers into three sets
S1, S2, S3 and determine some properties of these sets.