Published online by Cambridge University Press: 24 October 2008
This paper concerns, in the first instance, a sequence {t(1), t(2), t(3), …} of positive numbers denned successively by
where k ∈ ℕ = {1,2,3,…} and
Thus, when k is odd, A(k) consists of those divisors of k that do not exceed k/3; when k is even, A (k) consists of those even divisors n of k that make k/n odd and do not exceed k/3. The sets A(k) are listed in Table 1 for k ≤ 105; the numbers t(1) to t(10) are 1, 1, 4/3, 1, 6/5, 4/3, 8/7, 1, 14/9, 6/5.