On a problem of Erdős on integers, none of which divides the product of kk others

Erdős estimated the maximal number of integers selected from {1,2,…,N}{1,2,…,N}, so that none of them divides the product of two others. In this paper, Erdős’ problem is extended to sets of integers such that none of them divides the product of kk others. The proofs use combinatorial results.