Consider the n×n matrix with (i, j)’th entry gcd (i, j). Its largest eigenvalue \lambda _{n} and sum of entries s_{n} satisfy \lambda _{n} > s_{n}/n. Because sn cannot be expressed algebraically as a function of n, we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S.Hong, R.Loewy (2004). We also conjecture that \lambda _{n} > 6\Pi ^{-2}n log n for all n. If n is large enough, this follows from F.Balatoni (1969)., Jorma K. Merikoski., and Obsahuje seznam literatury