GCD sums and complete sets of square-free numbers

ahmad herdiat gunawan;

It is proved that
N
k,=1
gcd√(nk, n)
nkn
 N exp

C

logN log log logN
log logN
 holds for arbitrary integers 1 <= n1 < · · · < nN. This bound is essentially better than that found in a recent paper of Aistleitner, Berkes, and Seip and can be improved by no more than removal
of the triple logarithm. A certain completeness property of extremal sets of square-free numbers plays an important role in the proof of this result.