Abstrak

Kembali

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.