Maximal sets of numbers not containing k+1 pairwise coprimes and having divisors from a specified set of primes

摘要

We find the formula for the cardinality of a maximal set of integers from {1, ..., n} which does not contain k + 1 pairwise coprimes and each integer has a divisor from a specified set of r primes. We also find the explicit formula for this set, when r = k + 1. (c) 2006 Elsevier Inc. All rights reserved.